Related papers: Zeta-regularized vacuum expectation values from qu…
It has recently been shown that vacuum expectation values and Feynman path integrals can be regularized using Fourier integral operator $\zeta$-function, yet the physical meaning of these $\zeta$-regularized objects was unknown. Here we…
In recent work by the authors, a connection between Feynman's path integral and Fourier integral operator $\zeta$-functions has been established as a means of regularizing the vacuum expectation values in quantum field theories. However,…
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
A possible connection between quantum computing and Zeta functions of finite field equations is described. Inspired by the 'spectral approach' to the Riemann conjecture, the assumption is that the zeroes of such Zeta functions correspond to…
We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard…
This is a short guide to some uses of the zeta-function regularization procedure as a a basic mathematical tool for quantum field theory in curved space-time (as is the case of Nambu-Jona-Lasinio models), in quantum gravity models (in…
Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that…
The zeta-function regularization method is used to evaluate the renormalized effective action for massless conformally coupling scalar field propagating in a closed Friedman spacetime perturbed by a small rotation. To the second order of…
The Feynman Propagator of a charged particle confined to an anisotropic Harmonic Oscillator potential and moving in a crossed electromagnetic field is calculated in a conceptually new way. The calculation is based on the expansion of the…
A summary of relevant contributions, ordered in time, to the subject of operator zeta functions and their application to physical issues is provided. The description ends with the seminal contributions of Stephen Hawking and Stuart Dowker…
A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to…
Lattice field theory is a very powerful tool to study Feynman's path integral non-perturbatively. However, it usually requires Euclidean background metrics to be well-defined. On the other hand, a recently developed regularization scheme…
The vacuum fluctuations give rise to a number of phenomena; however, the the Casimir Effect is arguably the most salient manifestation of the quantum vacuum. In its most basic form it is realized through the interaction of a pair of neutral…
In this paper, we extend previous results on the quantum vacuum or Casimir energy, for a noninteracting rotating system and for an interacting nonrotating system, to the case where both rotation and interactions are present. Concretely, we…
An interesting example of the deep interrelation between Physics and Mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields. This procedure has recently been re-examined with care. Comments…
Spectral functions, such as the zeta functions, are widely used in Quantum Field Theory to calculate physical quantities. In this work, we compute the electrostatic potential and field due to an infinite discrete distribution of point…
It may be possible to use operator regularization with Feynman diagrams, which would greatly simplify its use as it has so far been limited to the more complicated Schwinger approach. Operator regularization, unlike $\zeta$-function…
Path integral quantization of quantum gauge general relativity is discussed in this paper. First, we deduce the generating functional of green function with external fields. Based on this generating functional, the propagators of…
We compute the quantum vacuum polarization for a pure neutral scalar field theory within the context of single-particle quantum mechanics. The loop diagram is computed without ever encountering loop-momentum integrals. Our approach is based…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…