In this work we investigate how the details of the quark-gluon interaction vertex affect the quan... more In this work we investigate how the details of the quark-gluon interaction vertex affect the quantitative description of chiral symmetry breaking and dynamical mass generation through the gap equation. We employ the Maris-Tandy (MT) [1] and Qin-Chang (QC) [2] models for the gluon propagator and the effective strong running coupling. The gap equation is solved by employing several vertex Ansätze which have been constructed in order to implement some of the key aspects of a gauge field theory such as gauge invariance and multiplicative renormalizability. We find that within a small variation of MT and QC model parameters, all truncations point towards the same quantitative pattern of chiral symmetry breaking, the running quark mass function, ensuring the robustness of this approach.
Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation func... more Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation functions within the class of linear covariant gauges. We derive the LKFT for the quark propagator and explicitly evaluate it up to the two loop level in the chiral limit. Although the number of diagrams to be evaluated is significantly larger than with the conventional computational scheme, the diagrams are simpler in nature, thereby leading to a considerably faster evaluation of the gauge dependent part than naively expected. Finally, we also resum the LKFT generated terms and compare our results with earlier work in the literature.
We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynami... more We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynamical symmetry breaking, in the light of its Landau-Khalatnikov-Fradkin transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. Carrying out a perturbative expansion of this result, it yields correct wavefunction renormalization and the mass function up to the terms independent of the gauge parameter. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution in Landau gauge in the rainbow approximation in terms of analytic functions. We then use LKFT to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have all the required qualitative features. We also go beyond the rainbow and encounter similar desirable qualitative features.
Schwinger-Dyson equations (SDEs) provide a natural staring point to study non-perturbative phenom... more Schwinger-Dyson equations (SDEs) provide a natural staring point to study non-perturbative phenomena such as dynamical chiral symmetry breaking in gauge field theories. We briefly review this research in the context of quenched quantum electrodynamics (QED) and discuss the advances made in the gradual improvement of the assumptions employed to solve these equations. We argue that these attempts render the corresponding studies more and more reliable and suitable for their future use in the more realistic cases of unquenched QED, quantum chromodynamics (QCD) and models alternative to the standard model of particle physics.
We study the dynamical generation of masses for fundamental fermions in quenched quantum electrod... more We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics in the presence of magnetic fields using Schwinger-Dyson equations. We show that, contrary to the case where the magnetic field is strong, in the weak field limit eB ≪ m(0) 2 , where m(0) is the value of the dynamically generated mass in the absence of the magnetic field, masses are generated above a critical value of the coupling and that this value is the same as in the case with no magnetic field. We carry out a numerical analysis to study the magnetic field dependence of the mass function above critical coupling and show that in this regime the dynamically generated mass and the chiral condensate for the lowest Landau level increase proportionally to (eB) 2 .
Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such ... more Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such as dynamical chiral symmetry breaking (DCSB). A reliable truncation of these equations leading to gauge invariant results is a challenging problem. Constraints imposed by Landau-Khalatnikov-Fradkin transformations (LKFT) can play an important role in the hunt for physically acceptable truncations. We present these constrains in the context of dynamical mass generation in QED in 2 + 1-dimensions.
We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum el... more We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum electrodynamics (QED3) considering four-component spinors with parity-even and parity-odd mass terms both for fermions and photons. Starting with its tree level expression in the Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge by means of its Landau-Khalatnikov-Fradkin transformation (LKFT). We compare our findings in the weak coupling regime with the direct one-loop calculation of the two-point Green function and observe perfect agreement up to a gauge independent term. We also reproduce results derived in earlier works as special cases of our findings. PACS numbers: 11.15.Tk,11.30.Er,12.20.-m Submitted to: J. Phys. A: Math. Gen. Gauge Covariance Relations and the Fermion Propagator in MCS-QED3 2 1.
We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge ... more We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge and dimension for Scalar Quantum Electrodynamics. Explicit results are presented for the particular cases of dimensions 3 and 4 both for massive and massless scalars. We then propose non-perturbative forms of this vertex that coincide with the perturbative answer to order e 2 .
We investigate the Compton scattering vertex of charged scalars and photons in scalar quantum ele... more We investigate the Compton scattering vertex of charged scalars and photons in scalar quantum electrodynamics (SQED). We carry out its non perturbative construction consistent with Ward-Fradkin-Green-Takahashi identity (WFGTI) which relates 3-point vertices to the 4-point ones. There is an undetermined part which is transverse to one or both the external photons, and needs to be evaluated through perturbation theory. We present in detail how the transverse part at the 1-loop order can be evaluated for completely general kinematics of momenta involved in covariant gauges and dimensions. This involves the calculation of genuine 4-point functions with three massive propagators, the most non-trivial integrals reported in this paper. We also discuss possible applications of our results.
This work is dedicated to the memory of Alfredo Raya Sr., guiding father, mentor and friend. Your... more This work is dedicated to the memory of Alfredo Raya Sr., guiding father, mentor and friend. Your legacy will live on in those whose lives you touched. Descanse en Paz. Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion-gauge-boson vertex is an important factor in deciding the issue.
For massless quenched QED in three dimensions, we evaluate a nonperturbative expression for the f... more For massless quenched QED in three dimensions, we evaluate a nonperturbative expression for the fermion propagator which agrees with its two loop perturbative expansion in the weak coupling regime. This calculation is carried out by making use of the Landau-Khalatnikov-Fradkin transformations. Any improved construction of the fermion-boson vertex must make sure that the solution of the Schwinger-Dyson equation for the fermion propagator reproduces this result. For two different gauges, we plot the fermion propagator against momentum. We then make a comparison with a similar plot, using the earlier expression for the fermion propagator, which takes into account only the one loop result.
We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases ... more We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavours N f. This is a necessary and sufficient consequence of the fact that there exists a critical value of electromagnetic coupling α beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in α to illustrate this. We study the flavour and coupling dependence of the dynamically generated mass analytically as well as numerically. We also derive the scaling laws for the dynamical mass as a function of α and N f. Up to a multiplicative constant, these scaling laws are related through (α, αc) ↔ (1/N f , 1/N c f). Calculation of the mass anomalous dimension γm shows that it is always greater than its value in the quenched case. We also evaluate the β-function. The criticality plane is drawn in the (α, N f) phase space which clearly depicts how larger N f is required to restore chiral symmetry for an increasing interaction strength.
A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahash... more A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED (qQED4) but also in its 3-dimensional counterpart (qQED3). Employing this convenient form of the vertex ansatz into the Schwinger-Dyson equation (SDE) for the fermion propagator, we observe that it renders the critical coupling in qQED4 markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and DCSB in qQED3.
We discuss the structure of the non-perturbative fermion-boson vertex in quenched QED. We show th... more We discuss the structure of the non-perturbative fermion-boson vertex in quenched QED. We show that it is possible to construct a vertex which not only ensures that the fermion propagator is multiplicatively renormalizable, obeys the appropriate Ward-Takahashi identity, reproduces perturbation theory for weak couplings and guarantees that the critical coupling at which the mass is dynamically generated is gauge independent but also makes sure that the value for the anomalous dimension for the mass function is strictly 1, as Holdom and Mahanta have proposed.
We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive ... more We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive QED3 through its one loop evaluation in an arbitrary covariant gauge. Written in a particular form, these constraints naturally lead us to the first non-perturbative construction of the vertex, which is in complete agreement with its one loop expansion in all momentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgoing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.
We study the dynamical generation of masses for fundamental fermions in quenched quantum electrod... more We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics (qQED) at finite temperature in the bare vertex approximation, using Schwinger-Dyson equations (SDE). Motivated by perturbation theory, a further simplification is introduced by taking the wave function renormalization to be unity. In the zeroth mode approximation, the SDE for the fermion propagator resembles QED in 2+1 dimensions (QED3) at zero temperature with an effective dimensionful coupling α ′ = αT. For a fixed temperature, mass is dynamically generated above a certain critical value of this coupling. As expected, raising the temperature restores chiral symmetry and fermions become massless again. We also argue that by summing over the frequency modes and under suitable simplifications, qualitative aspects of the result do not undergo significant changes.
We evaluate the fermion-photon vertex in QED at the one loop level in Hard Thermal Loop approxima... more We evaluate the fermion-photon vertex in QED at the one loop level in Hard Thermal Loop approximation and write it in covariant form. The complete vertex can be expanded in terms of 32 basis vectors. As is well known, the fermion-photon vertex and the fermion propagator are related through a Ward-Takahashi Identity (WTI). This relation splits the vertex into two parts: longitudinal (ΓL) and transverse (ΓT). ΓL is fixed by the WTI. The description of the longitudinal part consumes 8 of the basis vectors. The remaining piece ΓT is then written in terms of 24 spin amplitudes. Extending the work of Ball and Chiu and Kızılersü et. al., we propose a set of basis vectors T µ i (P1, P2) at finite temperature such that each of these is transverse to the photon four-momentum and also satisfies T µ i (P, P) = 0, in accordance with the Ward Identity, with their corresponding coefficients being free of kinematic singularities. This basis reduces to the form proposed by Kızılersü et. al. at zero temperature. We also evaluate explicitly the coefficient of each of these vectors at the above-mentioned level of approximation.
We present a workable model for the fermion-photon vertex, which is expressed solely in terms of ... more We present a workable model for the fermion-photon vertex, which is expressed solely in terms of functions that appear in the fermion propagator and independent of the angle between the relative momenta, and does not explicitly depend on the covariant-gauge parameter. It nevertheless produces a critical coupling for dynamical chiral symmetry breaking that is practically independent of the covariant-gauge parameter and an anomalous magnetic moment distribution for the dressed fermion that agrees in important respects with realistic numerical solutions of the inhomogeneous vector Bethe-Salpeter equation.
In this work we investigate how the details of the quark-gluon interaction vertex affect the quan... more In this work we investigate how the details of the quark-gluon interaction vertex affect the quantitative description of chiral symmetry breaking and dynamical mass generation through the gap equation. We employ the Maris-Tandy (MT) [1] and Qin-Chang (QC) [2] models for the gluon propagator and the effective strong running coupling. The gap equation is solved by employing several vertex Ansätze which have been constructed in order to implement some of the key aspects of a gauge field theory such as gauge invariance and multiplicative renormalizability. We find that within a small variation of MT and QC model parameters, all truncations point towards the same quantitative pattern of chiral symmetry breaking, the running quark mass function, ensuring the robustness of this approach.
Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation func... more Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation functions within the class of linear covariant gauges. We derive the LKFT for the quark propagator and explicitly evaluate it up to the two loop level in the chiral limit. Although the number of diagrams to be evaluated is significantly larger than with the conventional computational scheme, the diagrams are simpler in nature, thereby leading to a considerably faster evaluation of the gauge dependent part than naively expected. Finally, we also resum the LKFT generated terms and compare our results with earlier work in the literature.
We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynami... more We study the gauge dependence of the fermion propagator in quenched QED3, with and without dynamical symmetry breaking, in the light of its Landau-Khalatnikov-Fradkin transformation (LKFT). In the former case, starting with the massive bare propagator in the Landau gauge, we obtain non perturbative propagator in an arbitrary covariant gauge. Carrying out a perturbative expansion of this result, it yields correct wavefunction renormalization and the mass function up to the terms independent of the gauge parameter. Also, we obtain valuable information for the higher order perturbative expansion of the propagator. As for the case of dynamical chiral symmetry breaking, we start by approximating the numerical solution in Landau gauge in the rainbow approximation in terms of analytic functions. We then use LKFT to obtain the dynamically generated fermion propagator in an arbitrary covariant gauge. We find that the results obtained have all the required qualitative features. We also go beyond the rainbow and encounter similar desirable qualitative features.
Schwinger-Dyson equations (SDEs) provide a natural staring point to study non-perturbative phenom... more Schwinger-Dyson equations (SDEs) provide a natural staring point to study non-perturbative phenomena such as dynamical chiral symmetry breaking in gauge field theories. We briefly review this research in the context of quenched quantum electrodynamics (QED) and discuss the advances made in the gradual improvement of the assumptions employed to solve these equations. We argue that these attempts render the corresponding studies more and more reliable and suitable for their future use in the more realistic cases of unquenched QED, quantum chromodynamics (QCD) and models alternative to the standard model of particle physics.
We study the dynamical generation of masses for fundamental fermions in quenched quantum electrod... more We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics in the presence of magnetic fields using Schwinger-Dyson equations. We show that, contrary to the case where the magnetic field is strong, in the weak field limit eB ≪ m(0) 2 , where m(0) is the value of the dynamically generated mass in the absence of the magnetic field, masses are generated above a critical value of the coupling and that this value is the same as in the case with no magnetic field. We carry out a numerical analysis to study the magnetic field dependence of the mass function above critical coupling and show that in this regime the dynamically generated mass and the chiral condensate for the lowest Landau level increase proportionally to (eB) 2 .
Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such ... more Schwinger-Dyson equations (SDEs) are an ideal framework to study non-perturbative phenomena such as dynamical chiral symmetry breaking (DCSB). A reliable truncation of these equations leading to gauge invariant results is a challenging problem. Constraints imposed by Landau-Khalatnikov-Fradkin transformations (LKFT) can play an important role in the hunt for physically acceptable truncations. We present these constrains in the context of dynamical mass generation in QED in 2 + 1-dimensions.
We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum el... more We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum electrodynamics (QED3) considering four-component spinors with parity-even and parity-odd mass terms both for fermions and photons. Starting with its tree level expression in the Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge by means of its Landau-Khalatnikov-Fradkin transformation (LKFT). We compare our findings in the weak coupling regime with the direct one-loop calculation of the two-point Green function and observe perfect agreement up to a gauge independent term. We also reproduce results derived in earlier works as special cases of our findings. PACS numbers: 11.15.Tk,11.30.Er,12.20.-m Submitted to: J. Phys. A: Math. Gen. Gauge Covariance Relations and the Fermion Propagator in MCS-QED3 2 1.
We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge ... more We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge and dimension for Scalar Quantum Electrodynamics. Explicit results are presented for the particular cases of dimensions 3 and 4 both for massive and massless scalars. We then propose non-perturbative forms of this vertex that coincide with the perturbative answer to order e 2 .
We investigate the Compton scattering vertex of charged scalars and photons in scalar quantum ele... more We investigate the Compton scattering vertex of charged scalars and photons in scalar quantum electrodynamics (SQED). We carry out its non perturbative construction consistent with Ward-Fradkin-Green-Takahashi identity (WFGTI) which relates 3-point vertices to the 4-point ones. There is an undetermined part which is transverse to one or both the external photons, and needs to be evaluated through perturbation theory. We present in detail how the transverse part at the 1-loop order can be evaluated for completely general kinematics of momenta involved in covariant gauges and dimensions. This involves the calculation of genuine 4-point functions with three massive propagators, the most non-trivial integrals reported in this paper. We also discuss possible applications of our results.
This work is dedicated to the memory of Alfredo Raya Sr., guiding father, mentor and friend. Your... more This work is dedicated to the memory of Alfredo Raya Sr., guiding father, mentor and friend. Your legacy will live on in those whose lives you touched. Descanse en Paz. Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation (DSE) for the fermion self energy; i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed-fermion-gauge-boson vertex is an important factor in deciding the issue.
For massless quenched QED in three dimensions, we evaluate a nonperturbative expression for the f... more For massless quenched QED in three dimensions, we evaluate a nonperturbative expression for the fermion propagator which agrees with its two loop perturbative expansion in the weak coupling regime. This calculation is carried out by making use of the Landau-Khalatnikov-Fradkin transformations. Any improved construction of the fermion-boson vertex must make sure that the solution of the Schwinger-Dyson equation for the fermion propagator reproduces this result. For two different gauges, we plot the fermion propagator against momentum. We then make a comparison with a similar plot, using the earlier expression for the fermion propagator, which takes into account only the one loop result.
We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases ... more We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavours N f. This is a necessary and sufficient consequence of the fact that there exists a critical value of electromagnetic coupling α beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in α to illustrate this. We study the flavour and coupling dependence of the dynamically generated mass analytically as well as numerically. We also derive the scaling laws for the dynamical mass as a function of α and N f. Up to a multiplicative constant, these scaling laws are related through (α, αc) ↔ (1/N f , 1/N c f). Calculation of the mass anomalous dimension γm shows that it is always greater than its value in the quenched case. We also evaluate the β-function. The criticality plane is drawn in the (α, N f) phase space which clearly depicts how larger N f is required to restore chiral symmetry for an increasing interaction strength.
A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahash... more A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED (qQED4) but also in its 3-dimensional counterpart (qQED3). Employing this convenient form of the vertex ansatz into the Schwinger-Dyson equation (SDE) for the fermion propagator, we observe that it renders the critical coupling in qQED4 markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and DCSB in qQED3.
We discuss the structure of the non-perturbative fermion-boson vertex in quenched QED. We show th... more We discuss the structure of the non-perturbative fermion-boson vertex in quenched QED. We show that it is possible to construct a vertex which not only ensures that the fermion propagator is multiplicatively renormalizable, obeys the appropriate Ward-Takahashi identity, reproduces perturbation theory for weak couplings and guarantees that the critical coupling at which the mass is dynamically generated is gauge independent but also makes sure that the value for the anomalous dimension for the mass function is strictly 1, as Holdom and Mahanta have proposed.
We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive ... more We derive perturbative constraints on the transverse part of the fermion-boson vertex in massive QED3 through its one loop evaluation in an arbitrary covariant gauge. Written in a particular form, these constraints naturally lead us to the first non-perturbative construction of the vertex, which is in complete agreement with its one loop expansion in all momentum regimes. Without affecting its one-loop perturbative properties, we also construct an effective vertex in such a way that the unknown functions defining it have no dependence on the angle between the incoming and outgoing fermion momenta. Such a vertex should be useful for the numerical study of dynamical chiral symmetry breaking, leading to more reliable results.
We study the dynamical generation of masses for fundamental fermions in quenched quantum electrod... more We study the dynamical generation of masses for fundamental fermions in quenched quantum electrodynamics (qQED) at finite temperature in the bare vertex approximation, using Schwinger-Dyson equations (SDE). Motivated by perturbation theory, a further simplification is introduced by taking the wave function renormalization to be unity. In the zeroth mode approximation, the SDE for the fermion propagator resembles QED in 2+1 dimensions (QED3) at zero temperature with an effective dimensionful coupling α ′ = αT. For a fixed temperature, mass is dynamically generated above a certain critical value of this coupling. As expected, raising the temperature restores chiral symmetry and fermions become massless again. We also argue that by summing over the frequency modes and under suitable simplifications, qualitative aspects of the result do not undergo significant changes.
We evaluate the fermion-photon vertex in QED at the one loop level in Hard Thermal Loop approxima... more We evaluate the fermion-photon vertex in QED at the one loop level in Hard Thermal Loop approximation and write it in covariant form. The complete vertex can be expanded in terms of 32 basis vectors. As is well known, the fermion-photon vertex and the fermion propagator are related through a Ward-Takahashi Identity (WTI). This relation splits the vertex into two parts: longitudinal (ΓL) and transverse (ΓT). ΓL is fixed by the WTI. The description of the longitudinal part consumes 8 of the basis vectors. The remaining piece ΓT is then written in terms of 24 spin amplitudes. Extending the work of Ball and Chiu and Kızılersü et. al., we propose a set of basis vectors T µ i (P1, P2) at finite temperature such that each of these is transverse to the photon four-momentum and also satisfies T µ i (P, P) = 0, in accordance with the Ward Identity, with their corresponding coefficients being free of kinematic singularities. This basis reduces to the form proposed by Kızılersü et. al. at zero temperature. We also evaluate explicitly the coefficient of each of these vectors at the above-mentioned level of approximation.
We present a workable model for the fermion-photon vertex, which is expressed solely in terms of ... more We present a workable model for the fermion-photon vertex, which is expressed solely in terms of functions that appear in the fermion propagator and independent of the angle between the relative momenta, and does not explicitly depend on the covariant-gauge parameter. It nevertheless produces a critical coupling for dynamical chiral symmetry breaking that is practically independent of the covariant-gauge parameter and an anomalous magnetic moment distribution for the dressed fermion that agrees in important respects with realistic numerical solutions of the inhomogeneous vector Bethe-Salpeter equation.
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