August Romeo

Energy of the vacuum with a perfectly conducting and infinite cylindrical surface

Abstract Values for the vacuum energy of scalar fields under Dirichlet and Neumann boundary conditions on an infinite clylindrical surface are found, and they happen to be of opposite signs. In contrast with classical works, a complete zeta function regularization scheme is here applied. These fields are regarded as interesting both by themselves and as the key to describing the electromagnetic (e.m.) case. With their help, the figure for the e.m. Casimir effect in the presence of this surface, found by De Raad and Milton, is now confirmed.

Complete Zeta-Function Approach to the Electromagnetic Casimir Effect for Spheres and Circles

Abstract A method for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related zeta functions are central. Nontrivial results concerning these functions are given. While part of their application agrees with previous knowledge, new results like the zeta-regularized electromagnetic Casimir energy for a circular wire are included.

Multidimensional extension of a Wentzel–Kramers–Brillouin improvement for spherical quantum billiard zeta functions

Some insight is offered into the dimensional dependence of the Wentzel–Kramers–Brillouin (WKB) and improved‐WKB approximations introduced by Steiner in connection with hyperspherical (originally circular) quantum billiards. The accuracy of every new D‐dimensional picture is estimated by examining the residues of the spectral zeta‐function poles.

Photon propagation in space-time with a compactified spatial dimension

Abstract The one-loop effects of vacuum polarization induced by untwisted fermions in QED in a nonsimply connected space–time with topology S1×R3 are investigated. It is found that photon propagation in this system is anisotropic, appearing several massive photon modes and a superluminal transverse mode. For small compactification radius a, the superluminal velocity increases logarithmically with a. At low energies the photon masses lead to an effective confinement of the gauge fields into a (2+1)-dimensional manifold transverse to the compactified direction. The system shows a topologically induced directional superconductivity.

Regularized Casimir energy for an infinite dielectric cylinder subject to light-velocity conservation

Abstract The Casimir energy of a dilute dielectric cylinder, with the same light-velocity as in its surrounding medium, is evaluated exactly to first order in ξ 2 = e 1 −e 2 e 1 +e 2 2 (where e 1 , e 2 are the dielectric constants of the cylinder and of its environment), and numerically to higher orders in ξ 2 . The first part is carried out using addition formulas for Bessel functions, and no Debye expansions are required.

Manifestations of Quantum Gravity in Scalar QED Phenomena

Quantum gravitational corrections to the effective potential, at the one-loop level and in the leading-log approximation, for scalar quantum electrodynamics with higher-derivative gravity, which is taken as an effective theory for quantum gravity (QG), are calculated. We point out the appearance of relevant phenomena caused by quantum gravity, such as dimensional transmutation, QG-driven instabilities of the potential, QG corrections to scalar-to-vector mass ratios, and curvature-induced phase transitions, whose existence is shown by means of analytical and numerical study.

Renormalization group properties of higher-derivative quantum gravity with matter in 4 - ε dimensions

Abstract We investigate the phase structure and the infrared properties of higher-derivative quantum gravity (QG) with matter, in 4 - e dimensions. The renormalization group (RG) equations in 4 - e dimensions are analysed for the following types of matter: the fϕ 4 theory, the O ( N ) ϕ 4 theory, scalar electrodynamics, and the SU (2) model with scalars. New fixed points for the scalar coupling appear—one of which is IR stable—some of them being induced by QG. The IR stable fixed point perturbed by QG leads to a second-order phase transition for the theory at non-zero temperature. The RG improved effective potential in the SU (2) theory (which can be considered as the confining phase of the standard model) is calculated at non-zero temperature and it is shown that its shape is clearly influenced by QG.

Black hole entropy and effective potential

The free energy and entropy for a non-extremal Reissner - Nordstrom black hole are studied by zeta-function regularization in WKB approximation. Their leading divergences agree with the Susskind - Uglum predictions. Logarithmic singularities appear in connection with the Seeley - De Witt coefficient for the scale anomaly. The equivalence between the small- approximation and the optical space approach is checked. After taking advantage of renormalization group methods, effective potentials are considered for a scalar field with a self-interaction and scalar electrodynamics, both of them on a Schwarzschild background. Numerical study of the potential at the event horizon shows symmetry breaking, and we argue that in some conditions this effect may be a purely quantal one.

Zeta‐regularization of the O(N) nonlinear sigma model in D dimensions

The O(N) nonlinear sigma model in a D‐dimensional space of the form RD−M×TM, RD−M×SM, or TM×SP is studied, where RM, TM, and SM correspond to flat space, a torus, and a sphere, respectively. Using zeta‐regularization and the 1/N expansion, the corresponding partition functions—for deriving the free energy—and the gap equations are obtained. In particular, the free energy at the critical point on R2q+1×S2p+2 vanishes in accordance with the conformal equivalence to the flat space RD. Numerical solutions of the gap equations at the critical coupling constants are given for several values of D. The properties of the partition function and its asymptotic behavior for large D are discussed. In a similar way, a higher‐derivative nonlinear sigma model is investigated, too. The physical relevance of our results is discussed.

Spontaneous CPT violation in confined QED

Symmetry breaking effects induced by untwisted fermions in QED in a nonsimply connected spacetime with topology S1×R3 is investigated. It is found that the discrete CPT symmetry of the theory is spontaneously broken by the appearance of a constant vacuum expectation value of the electromagnetic potential along the direction of space periodicity. The constant potential is shown to be gauge nonequivalent to zero in the nonsimply connected spacetime under consideration. Due to the symmetry breaking, one of the electromagnetic modes of propagation is massive with a mass that depends on the inverse of the compactification length. As a result the system exhibits a sort of topological directional superconductivity. A second electromagnetic mode is superluminal, with a superluminal velocity that increases logarithmically with the compactification radius.