arXiv subjects

Alexander Yu. Kamenshchik

Publications and source records attributed to Alexander Yu. Kamenshchik.

62 records · Page 4Linked to original sources

arXiv1996

One-Loop Effective Action for Euclidean Maxwell Theory on Manifolds with Boundary

This paper studies the one-loop effective action for Euclidean Maxwell theory about flat four-space bounded by one three-sphere, or two concentric three-spheres. The analysis relies on Faddeev-Popov formalism and $ζ$-function regularization, and the Lorentz gauge-averaging term is used with magnetic boundary conditions. The contributions of transverse, longitudinal and normal modes of the electromagnetic potential, jointly with ghost modes, are derived in detail. The most difficult part of the analysis consists in the eigenvalue condition given by the determinant of a $2 \times 2$ or $4 \times 4$ matrix for longitudinal and normal modes. It is shown that the former splits into a sum of Dirichlet and Robin contributions, plus a simpler term. This is the quantum cosmological case. In the latter case, however, when magnetic boundary conditions are imposed on two bounding three-spheres, the determinant is more involved. Nevertheless, it is evaluated explicitly as well. The whole analysis provides the building block for studying the one-loop effective action in covariant gauges, on manifolds with boundary. The final result differs from the value obtained when only transverse modes are quantized, or when noncovariant gauges are used.

hep-th↗

arXiv1996

Boundary Operators in Euclidean Quantum Gravity

Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that, on choosing the de Donder functional, the resulting boundary operator involves projection operators jointly with a nilpotent operator. Moreover, the elliptic operator acting on metric perturbations is symmetric. Other choices of mixed boundary conditions, for which the normal components of metric perturbations can be set to zero at the boundary, are then analyzed in detail. Last, the evaluation of the 1-loop divergence in the axial gauge for gravity is obtained. Interestingly, such a divergence turns out to coincide with the one resulting from transverse-traceless perturbations.

hep-th↗

arXiv1996

One-Loop Effective Action on the Four-Ball

This paper applies $ζ$-function regularization to evaluate the 1-loop effective action for scalar field theories and Euclidean Maxwell theory in the presence of boundaries. After a comparison of two techniques developed in the recent literature, vacuum Maxwell theory is studied and the contribution of all perturbative modes to $ζ'(0)$ is derived: transverse, longitudinal and normal modes of the electromagnetic potential, jointly with ghost modes. The analysis is performed on imposing magnetic boundary conditions, when the Faddeev-Popov Euclidean action contains the particular gauge-averaging term which leads to a complete decoupling of all perturbative modes. It is shown that there is no cancellation of the contributions to $ζ'(0)$ resulting from longitudinal, normal and ghost modes.

hep-th↗

arXiv1995

Spin-3/2 Potentials in Backgrounds with Boundary

This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional Riemannian backgrounds with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing the background is Ricci-flat, in agreement with previous results in the literature. However, the preservation of boundary conditions under such gauge transformations leads to a restriction of the gauge freedom. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then applied. The equations for the secondary potentials, jointly with the boundary conditions, imply that the background four-geometry is further restricted to be totally flat. The analysis of other gauge transformations confirms that, in the massless case, the only admissible class of Riemannian backgrounds with boundary is totally flat.

gr-qc↗

arXiv1995

Mixed Boundary Conditions in Euclidean Quantum Gravity

This paper studies a new set of mixed boundary conditions in Euclidean quantum gravity. These involve, in particular, Robin boundary conditions on the perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on the whole ghost 1-form. The corresponding trace anomaly is evaluated in the case of flat Euclidean 4-space bounded by a 3-sphere. In general, this anomaly differs from the ones resulting from other local or non-local boundary conditions studied in the recent literature.

gr-qc↗

arXiv1995

Gravitons in One-Loop Quantum Cosmology: Correspondence Between Covariant and Non-Covariant Formalisms

The discrepancy between the results of covariant and non-covariant one-loop calculations for higher-spin fields in quantum cosmology is analyzed. A detailed mode-by-mode study of perturbative quantum gravity about a flat Euclidean background bounded by two concentric 3-spheres, including non-physical degrees of freedom and ghost modes, leads to one-loop amplitudes in agreement with the covariant Schwinger-DeWitt method. This calculation provides the generalization of a previous analysis of fermionic fields and electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a well-defined 3+1 decomposition.

gr-qc↗

arXiv1995

Coulomb Gauge in One-Loop Quantum Cosmology

The well-known discrepancies between covariant and non-covariant formalisms in quantum field theory and quantum cosmology are analyzed by focusing on the Coulomb gauge for vacuum Maxwell theory. On studying a flat Euclidean background with boundaries, the corresponding mode-by-mode analysis of one-loop quantum amplitudes agrees with the results of the Schwinger-DeWitt technique and of mode-by-mode calculations in relativistic gauges.

gr-qc↗

arXiv1995

Euclidean Maxwell Theory in the Presence of Boundaries. II

Zeta-function regularization is applied to complete a recent analysis of the quantized electromagnetic field in the presence of boundaries. The quantum theory is studied by setting to zero on the boundary the magnetic field, the gauge-averaging functional and hence the Faddeev-Popov ghost field. Electric boundary conditions are also studied. On considering two gauge functionals which involve covariant derivatives of the 4-vector potential, a series of detailed calculations shows that, in the case of flat Euclidean 4-space bounded by two concentric 3-spheres, one-loop quantum amplitudes are gauge independent and their mode-by-mode evaluation agrees with the covariant formulae for such amplitudes and coincides for magnetic or electric boundary conditions. By contrast, if a single 3-sphere boundary is studied, one finds some inconsistencies, i.e. gauge dependence of the amplitudes.

gr-qc↗