Quantized Maxwell Theory in a Conformally Invariant Gauge

Maxwell theory can be studied in a gauge which is invariant under conformal rescalings of the metric, and first proposed by Eastwood and Singer. This paper studies the corresponding quantization in flat Euclidean 4-space. The resulting ghost operator is a fourth-order elliptic operator, while the operator P on perturbations of the potential is a sixth-order elliptic operator. The operator P may be reduced to a second-order non-minimal operator if a dimensionless gauge parameter tends to infinity. Gauge-invariant boundary conditions are obtained by setting to zero at the boundary the whole set of perturbations of the potential, jointly with ghost perturbations and their normal derivative. This is made possible by the fourth-order nature of the ghost operator. An analytic representation of the ghost basis functions is also obtained.Comment: 8 pages, plain Tex. In this revised version, the calculation of ghost basis functions has been amended, and the presentation has been improve

Boundary Operators in Quantum Field Theory

The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this programme, the present paper shows under which conditions the introduction of pseudo-differential boundary operators in one-loop Euclidean quantum gravity is compatible both with their invariance under infinitesimal diffeomorphisms and with the requirement of a strongly elliptic theory. Suitable assumptions on the kernel of the boundary operator make it therefore possible to overcome problems resulting from the choice of purely local boundary conditions.Comment: 23 pages, plain Tex. The revised version contains a new section, and the presentation has been improve

Radiation Induced Fermion Resonance

The Dirac equation is solved for two novel terms which describe the interaction energy between the half integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms and the existence of radiation induced fermion resonance.Comment: latex, 4 pages, no figure

Singularity Theory in Classical Cosmology

This paper compares recent approaches appearing in the literature on the singularity problem for space-times with nonvanishing torsion.Comment: 4 pages, plain-tex, published in Nuovo Cimento B, volume 107, pages 849-851, year 199

New Developments in the Spectral Asymptotics of Quantum Gravity

A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory. All of this is made possible by a peculiar spectral cancellation on the Euclidean 4-ball, here derived and discussed.Comment: 7 pages, latex file. Paper prepared for the Conference "QFEXT05: Quantum Field Theory Under the Influence of External Conditions", Barcelona, September 5 - September 9, 2005. In the final version, the presentation has been further improved, and yet other References have been adde

Non-Locality and Ellipticity in a Gauge-Invariant Quantization

The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary conditions. If the Robin sector is modified by the addition of a pseudo-differential boundary operator, gauge-invariant boundary conditions are obtained at the price of dealing with gauge-field and ghost operators which become pseudo-differential. A good elliptic theory is then obtained if the kernel occurring in the boundary operator obeys certain summability conditions, and it leads to a peculiar form of the asymptotic expansion of the symbol. The cases of ghost operator of negative and positive order are studied within this framework.Comment: 17 pages, plain Te

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 $\zeta$-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.Comment: 25 pages, Revte