We calculate the one-loop corrections to the free energy and to the entropy for fields with arbit... more We calculate the one-loop corrections to the free energy and to the entropy for fields with arbitrary spins in the space $S^1\otimes H^N$. For conformally invariant fields by means of a conformal transformation of the metric the results are valid in Rindler space with $D=N+1$ dimensions. We use the zeta regularization technique which yields an ultraviolet finite result for the
We calculate the low temperature corrections to the free energy for a sphere in front of a plane.... more We calculate the low temperature corrections to the free energy for a sphere in front of a plane. First, the scalar field obeying Dirichet or Neumann boundary conditions is considered. Second, the electromagnetic field is studied, the sphere being perfectly conducting and being a dielectric ball with both, constant permittivity and permittivity of the plasma model.
The Casimir energy corresponding to a massive scalar field with Dirichlet bound- ary conditions o... more The Casimir energy corresponding to a massive scalar field with Dirichlet bound- ary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular the differences occurring with respect to the case when the field occupies the
We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We ... more We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We fix ambiguities by the renormalization condition that the quantum mass vanishes as one lets the mass gap tend to infinity while keeping scattering data fixed. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and
We calculate the constraints on the constants of hypothetical long-range interactions which follo... more We calculate the constraints on the constants of hypothetical long-range interactions which follow from the recent measurement of the Casimir force. A comparison with previous constraints is given. The new constraints are up to a factor of 3000 stronger in some parameter regions. {copyright} {ital 1997} {ital The American Physical Society}
The dependence of the van der Waals force on the distance between the atomic force microscope tip... more The dependence of the van der Waals force on the distance between the atomic force microscope tip and the plane surface of the sample is calculated. The tip is modelled by a paraboloid with stochastic perturbations of its surface. The analysis of the corresponding corrections to the van der Waals force shows that one may use the paraboloid model of
... xii Contents 11.2.2 Four-dimensional spacetime 268 11.3 Nontrivial topologies in cosmology 2... more ... xii Contents 11.2.2 Four-dimensional spacetime 268 11.3 Nontrivial topologies in cosmology 270 11.4 Compactification of extra dimensions 274 11.5 Topological defects 276 II THE CASIMIR FORCE BETWEEN REAL BODIES 12 The Lifshitz theory of the van der Waals and ...
The leading radiative correction to the Casimir energy for two parallel penetrable mirrors is cal... more The leading radiative correction to the Casimir energy for two parallel penetrable mirrors is calculated within QED perturbation theory. It is found to be of the order α like the known radiative correction for ideally reflecting mirrors from which it differs only by a monotonic, powerlike function of the frequency at which the mirrors become transparent. This shows that the O(α 2 ) radiative correction calculated recently by Kong and Ravndal for ideally reflecting mirrors on the basis of effective field theory methods remains subleading even for the physical case of penetrable mirrors.
We find the joint effect of non-zero temperature and finite conductivity onto the Casimir force b... more We find the joint effect of non-zero temperature and finite conductivity onto the Casimir force between real metals. Configurations of two parallel plates and a sphere (lens) above a plate are considered. Perturbation theory in two parameters (the relative temperature and the relative penetration depth of zero point oscillations into the metal) is developed. Perturbative results are compared with computations. Recent evidence concerning possible existence of large temperature corrections at small separations between the real metals is not supported.
We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar ... more We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar and electromagnetic fields and calculate the limiting cases. For small separation we compare the exact results with the corresponding ones obtained in proximity force approximation. For the scalar field with Dirichlet boundary conditions, the low temperature correction is of order T 2 like for parallel planes. For the electromagnetic field it is of order T 4 . For high temperature we observe the usual picture that the leading order is given by the zeroth Matsubara frequency. The non-zero frequencies are exponentially suppressed except for the case of close separation. PACS numbers: 03.70.+k Theory of quantized fields 11.10.Wx Finite-temperature field theory 11.80.La Multiple scattering 12.20.Ds Specific calculations a [email protected] b [email protected]
We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying t... more We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying the conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio . This correction is of order . Opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, ln and (ln)². We compare this result with the available findings of numerical and experimental approaches.
We develop a formalism for the calculation of the ground state energy of a spinor field in the ba... more We develop a formalism for the calculation of the ground state energy of a spinor field in the background of a cylindrically symmetric magnetic field. The energy is expressed in terms of the Jost function of the associated scattering problem. Uniform asymptotic expansions needed are obtained from the Lippmann-Schwinger equation. The general results derived are applied to the background of a finite radius flux tube with a homogeneous magnetic field inside and the ground state energy is calculated numerically as a function of the radius and the flux. It turns out to be negative, remaining smaller by a factor of α than the classical energy of the background except for very small values of the radius which are outside the range of applicability of QED
The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is... more The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is calculated. The calculation is performed in the framework of covariant perturbation theory with the boundary conditions implemented as constraints. The formalism is briefly reviewed and its use is explained by deriving the known results for two parallel planes.
The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to... more The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel coefficients and the related determinant. For this, some new heat kernel coefficients and determinants had to be calculated for the boundary conditions under consideration. The obtained results reproduce all the asymptotics derived by other methods in the problems at hand and involve a few new terms in the high temperature expansions. An obvious merit of this approach is its universality and applicability to any boundary value problem correctly formulated. 12.20.Ds, 03.70.+k, 78.60.Mq, 42.50.Lc
The vacuum energy of a scalar field in a spherically symmetric background field is considered. It... more The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in an simple explicit example.
We calculate the vacuum energy of a spinor field in the background of a Nielsen-Olesen vortex. We... more We calculate the vacuum energy of a spinor field in the background of a Nielsen-Olesen vortex. We use the method of representing the vacuum energy in terms of the Jost function on the imaginary momentum axis. Renormalization is carried out using the heat kernel expansion and zeta functional regularization. With this method well convergent sums and integrals emerge which allow for an efficient numerical calculation of the vacuum energy in the given case where the background is not known analytically but only numerically. The vacuum energy is calculated for several choices of the parameters and it turns out to give small corrections to the classical energy. *
The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on ... more The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular the differences occurring with respect to the case when the field occupies the whole space. The final result contains several constants that experience renormalization and can be determined only experimentally. The non-trivial finite parts that appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time.
We calculate the one-loop corrections to the free energy and to the entropy for fields with arbit... more We calculate the one-loop corrections to the free energy and to the entropy for fields with arbitrary spins in the space $S^1\otimes H^N$. For conformally invariant fields by means of a conformal transformation of the metric the results are valid in Rindler space with $D=N+1$ dimensions. We use the zeta regularization technique which yields an ultraviolet finite result for the
We calculate the low temperature corrections to the free energy for a sphere in front of a plane.... more We calculate the low temperature corrections to the free energy for a sphere in front of a plane. First, the scalar field obeying Dirichet or Neumann boundary conditions is considered. Second, the electromagnetic field is studied, the sphere being perfectly conducting and being a dielectric ball with both, constant permittivity and permittivity of the plasma model.
The Casimir energy corresponding to a massive scalar field with Dirichlet bound- ary conditions o... more The Casimir energy corresponding to a massive scalar field with Dirichlet bound- ary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular the differences occurring with respect to the case when the field occupies the
We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We ... more We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We fix ambiguities by the renormalization condition that the quantum mass vanishes as one lets the mass gap tend to infinity while keeping scattering data fixed. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and
We calculate the constraints on the constants of hypothetical long-range interactions which follo... more We calculate the constraints on the constants of hypothetical long-range interactions which follow from the recent measurement of the Casimir force. A comparison with previous constraints is given. The new constraints are up to a factor of 3000 stronger in some parameter regions. {copyright} {ital 1997} {ital The American Physical Society}
The dependence of the van der Waals force on the distance between the atomic force microscope tip... more The dependence of the van der Waals force on the distance between the atomic force microscope tip and the plane surface of the sample is calculated. The tip is modelled by a paraboloid with stochastic perturbations of its surface. The analysis of the corresponding corrections to the van der Waals force shows that one may use the paraboloid model of
... xii Contents 11.2.2 Four-dimensional spacetime 268 11.3 Nontrivial topologies in cosmology 2... more ... xii Contents 11.2.2 Four-dimensional spacetime 268 11.3 Nontrivial topologies in cosmology 270 11.4 Compactification of extra dimensions 274 11.5 Topological defects 276 II THE CASIMIR FORCE BETWEEN REAL BODIES 12 The Lifshitz theory of the van der Waals and ...
The leading radiative correction to the Casimir energy for two parallel penetrable mirrors is cal... more The leading radiative correction to the Casimir energy for two parallel penetrable mirrors is calculated within QED perturbation theory. It is found to be of the order α like the known radiative correction for ideally reflecting mirrors from which it differs only by a monotonic, powerlike function of the frequency at which the mirrors become transparent. This shows that the O(α 2 ) radiative correction calculated recently by Kong and Ravndal for ideally reflecting mirrors on the basis of effective field theory methods remains subleading even for the physical case of penetrable mirrors.
We find the joint effect of non-zero temperature and finite conductivity onto the Casimir force b... more We find the joint effect of non-zero temperature and finite conductivity onto the Casimir force between real metals. Configurations of two parallel plates and a sphere (lens) above a plate are considered. Perturbation theory in two parameters (the relative temperature and the relative penetration depth of zero point oscillations into the metal) is developed. Perturbative results are compared with computations. Recent evidence concerning possible existence of large temperature corrections at small separations between the real metals is not supported.
We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar ... more We consider the Casimir effect for a sphere in front of a plane at finite temperature for scalar and electromagnetic fields and calculate the limiting cases. For small separation we compare the exact results with the corresponding ones obtained in proximity force approximation. For the scalar field with Dirichlet boundary conditions, the low temperature correction is of order T 2 like for parallel planes. For the electromagnetic field it is of order T 4 . For high temperature we observe the usual picture that the leading order is given by the zeroth Matsubara frequency. The non-zero frequencies are exponentially suppressed except for the case of close separation. PACS numbers: 03.70.+k Theory of quantized fields 11.10.Wx Finite-temperature field theory 11.80.La Multiple scattering 12.20.Ds Specific calculations a [email protected] b [email protected]
We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying t... more We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying the conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio . This correction is of order . Opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, ln and (ln)². We compare this result with the available findings of numerical and experimental approaches.
We develop a formalism for the calculation of the ground state energy of a spinor field in the ba... more We develop a formalism for the calculation of the ground state energy of a spinor field in the background of a cylindrically symmetric magnetic field. The energy is expressed in terms of the Jost function of the associated scattering problem. Uniform asymptotic expansions needed are obtained from the Lippmann-Schwinger equation. The general results derived are applied to the background of a finite radius flux tube with a homogeneous magnetic field inside and the ground state energy is calculated numerically as a function of the radius and the flux. It turns out to be negative, remaining smaller by a factor of α than the classical energy of the background except for very small values of the radius which are outside the range of applicability of QED
The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is... more The first radiative correction to the Casimir energy of a perfectly conducting spherical shell is calculated. The calculation is performed in the framework of covariant perturbation theory with the boundary conditions implemented as constraints. The formalism is briefly reviewed and its use is explained by deriving the known results for two parallel planes.
The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to... more The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel coefficients and the related determinant. For this, some new heat kernel coefficients and determinants had to be calculated for the boundary conditions under consideration. The obtained results reproduce all the asymptotics derived by other methods in the problems at hand and involve a few new terms in the high temperature expansions. An obvious merit of this approach is its universality and applicability to any boundary value problem correctly formulated. 12.20.Ds, 03.70.+k, 78.60.Mq, 42.50.Lc
The vacuum energy of a scalar field in a spherically symmetric background field is considered. It... more The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in an simple explicit example.
We calculate the vacuum energy of a spinor field in the background of a Nielsen-Olesen vortex. We... more We calculate the vacuum energy of a spinor field in the background of a Nielsen-Olesen vortex. We use the method of representing the vacuum energy in terms of the Jost function on the imaginary momentum axis. Renormalization is carried out using the heat kernel expansion and zeta functional regularization. With this method well convergent sums and integrals emerge which allow for an efficient numerical calculation of the vacuum energy in the given case where the background is not known analytically but only numerically. The vacuum energy is calculated for several choices of the parameters and it turns out to give small corrections to the classical energy. *
The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on ... more The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary to apply in each situation is studied in detail, in particular the differences occurring with respect to the case when the field occupies the whole space. The final result contains several constants that experience renormalization and can be determined only experimentally. The non-trivial finite parts that appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time.
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Papers by Michael Bordag