Based on the non-relativistic regime of the Dirac equation coupled to a torsion pseudo-vector, we... more Based on the non-relativistic regime of the Dirac equation coupled to a torsion pseudo-vector, we study the dynamics of magnetization and how it is affected by the presence of torsion. We consider that torsion interacting terms in Dirac equation appear in two ways one of these is thhrough the covariant derivative considering the spin connection and gauge magnetic field and the other is through a non-minimal spin torsion coupling. We show within this framework, that it is possible to obtain the most general Landau, Lifshitz and Gilbert (LLG) equation including the torsion effects, where we refer to torsion as a geometric field playing an important role in the spin coupling process. We show that the torsion terms can give us two important landscapes in the magnetization dynamics: one of them related with damping and the other related with the screw dislocation that give us a global effect like a helix damping sharped. These terms are responsible for changes in the magnetization preces...
In this paper, following a stream of investigation of supersymetric gauge theories with cosmic st... more In this paper, following a stream of investigation of supersymetric gauge theories with cosmic string solutions, we contemplate the possibility of building up a superconducting cosmic string with a gauge-field mixing in conection with to a U(1) × U(1)′symmetry. Both spontaneous breakings, of gauge and supersymmetry, are thoroughly analysed and the fermion zero-modes are worked out. The rôle of the gauge-field mixing parameter is elucidated in conection with the string configuration. [email protected][email protected][email protected] 1
We construct a class of knot solutions of the gravitoelectromagnetic (GEM) equations in vacuum in... more We construct a class of knot solutions of the gravitoelectromagnetic (GEM) equations in vacuum in the linearized gravity approximation by analogy with the Rañada-Hopf fields. For these solutions, the dual metric tensors of the bi-metric geometry of the gravitational vacuum with knot perturbations are given and the geodesic equation as a function of two complex parameters of the GEM knots are calculated. Finally, the Landau–Lifshitz pseudo-tensor and a scalar invariant of the GEM knots are computed. ar X iv :2 10 3. 00 21 7v 1 [ gr -q c] 2 7 Fe b 20 21
One has recently presented an extension of the standard variational calculus to include the prese... more One has recently presented an extension of the standard variational calculus to include the presence of deformed derivatives, both in the Lagrangian of systems of particles and in the Lagrangian density of field-theoretic models. Classical Euler-Lagrange equations and the Hamiltonian formalism have been reassessed in this approach. Whenever applied to a number of physical systems, the resulting dynamical equations come out to be the correct ones found in the literature, especially with mass-dependent and with nonlinear equations for classical and quantum-mechanical systems. In the present contribution, one extends the variational approach, including a piecewise form of deformed derivatives to study higher-order dissipative systems and to obtain, as an option, deformed equations as well. Applications to concrete situations are contemplated, such as an accelerated point charge—this is the problem of the Abraham-Lorentz-Dirac force—stochastic dynamics like the Langevin, the advection-c...
Our main interest here is to analyze the gauge invariance issue concerning the noncommutative rel... more Our main interest here is to analyze the gauge invariance issue concerning the noncommutative relativistic particle. Since the analysis of the constraint set from Dirac’s point of view classifies it as a second-class system, it is not a gauge theory. Hence, the objective here is to obtain gauge invariant actions linked to the original one. However, we have two starting points, meaning that firstly we will begin directly from the original action and, using the Noether procedure, we have obtained a specific dual (gauge invariant) action. Following another path, we will act towards the constraints so that we have carried out the conversion of second to first-class constraints through the Batalin–Fradkin–Fradkina–Tyutin formalism, obtaining the second gauge invariant Lagrangian.
Starting from a field theory action that describes a Dirac fermion, we propose and analyze a mode... more Starting from a field theory action that describes a Dirac fermion, we propose and analyze a model based on a low‐relativistic Pauli equation coupled to a torsion‐like term to study Spin Hall Effect (SHE). We point out a very particular connection between the modified Pauli equation and the (SHE), where what we refer to torsion as field playing an important role in the spin‐orbit (SO) coupling process. In this scenario, we present a proposal of a spin‐type current, considering the tiny contributions of torsion in connection with intrinsic anisotropy of the crystal electric field.
Constrained systems are fundamental to understanding of several physical realities. Even so the H... more Constrained systems are fundamental to understanding of several physical realities. Even so the Hall effect is one of more revisited issue we can still find new approaches to obtain old and new important relations. In this paper a semi classical formulation is considered where an Chern-Simons gauge invariant theory is constructed for a Schroedinger field. The main idea is to
Based on the non-relativistic regime of the Dirac equation coupled to a torsion pseudo-vector, we... more Based on the non-relativistic regime of the Dirac equation coupled to a torsion pseudo-vector, we study the dynamics of magnetization and how it is affected by the presence of torsion. We consider that torsion interacting terms in Dirac equation appear in two ways one of these is thhrough the covariant derivative considering the spin connection and gauge magnetic field and the other is through a non-minimal spin torsion coupling. We show within this framework, that it is possible to obtain the most general Landau, Lifshitz and Gilbert (LLG) equation including the torsion effects, where we refer to torsion as a geometric field playing an important role in the spin coupling process. We show that the torsion terms can give us two important landscapes in the magnetization dynamics: one of them related with damping and the other related with the screw dislocation that give us a global effect like a helix damping sharped. These terms are responsible for changes in the magnetization preces...
In this paper, following a stream of investigation of supersymetric gauge theories with cosmic st... more In this paper, following a stream of investigation of supersymetric gauge theories with cosmic string solutions, we contemplate the possibility of building up a superconducting cosmic string with a gauge-field mixing in conection with to a U(1) × U(1)′symmetry. Both spontaneous breakings, of gauge and supersymmetry, are thoroughly analysed and the fermion zero-modes are worked out. The rôle of the gauge-field mixing parameter is elucidated in conection with the string configuration. [email protected][email protected][email protected] 1
We construct a class of knot solutions of the gravitoelectromagnetic (GEM) equations in vacuum in... more We construct a class of knot solutions of the gravitoelectromagnetic (GEM) equations in vacuum in the linearized gravity approximation by analogy with the Rañada-Hopf fields. For these solutions, the dual metric tensors of the bi-metric geometry of the gravitational vacuum with knot perturbations are given and the geodesic equation as a function of two complex parameters of the GEM knots are calculated. Finally, the Landau–Lifshitz pseudo-tensor and a scalar invariant of the GEM knots are computed. ar X iv :2 10 3. 00 21 7v 1 [ gr -q c] 2 7 Fe b 20 21
One has recently presented an extension of the standard variational calculus to include the prese... more One has recently presented an extension of the standard variational calculus to include the presence of deformed derivatives, both in the Lagrangian of systems of particles and in the Lagrangian density of field-theoretic models. Classical Euler-Lagrange equations and the Hamiltonian formalism have been reassessed in this approach. Whenever applied to a number of physical systems, the resulting dynamical equations come out to be the correct ones found in the literature, especially with mass-dependent and with nonlinear equations for classical and quantum-mechanical systems. In the present contribution, one extends the variational approach, including a piecewise form of deformed derivatives to study higher-order dissipative systems and to obtain, as an option, deformed equations as well. Applications to concrete situations are contemplated, such as an accelerated point charge—this is the problem of the Abraham-Lorentz-Dirac force—stochastic dynamics like the Langevin, the advection-c...
Our main interest here is to analyze the gauge invariance issue concerning the noncommutative rel... more Our main interest here is to analyze the gauge invariance issue concerning the noncommutative relativistic particle. Since the analysis of the constraint set from Dirac’s point of view classifies it as a second-class system, it is not a gauge theory. Hence, the objective here is to obtain gauge invariant actions linked to the original one. However, we have two starting points, meaning that firstly we will begin directly from the original action and, using the Noether procedure, we have obtained a specific dual (gauge invariant) action. Following another path, we will act towards the constraints so that we have carried out the conversion of second to first-class constraints through the Batalin–Fradkin–Fradkina–Tyutin formalism, obtaining the second gauge invariant Lagrangian.
Starting from a field theory action that describes a Dirac fermion, we propose and analyze a mode... more Starting from a field theory action that describes a Dirac fermion, we propose and analyze a model based on a low‐relativistic Pauli equation coupled to a torsion‐like term to study Spin Hall Effect (SHE). We point out a very particular connection between the modified Pauli equation and the (SHE), where what we refer to torsion as field playing an important role in the spin‐orbit (SO) coupling process. In this scenario, we present a proposal of a spin‐type current, considering the tiny contributions of torsion in connection with intrinsic anisotropy of the crystal electric field.
Constrained systems are fundamental to understanding of several physical realities. Even so the H... more Constrained systems are fundamental to understanding of several physical realities. Even so the Hall effect is one of more revisited issue we can still find new approaches to obtain old and new important relations. In this paper a semi classical formulation is considered where an Chern-Simons gauge invariant theory is constructed for a Schroedinger field. The main idea is to
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