Related papers: Zeta-regularized vacuum expectation values
The vacuum angle $\theta$ renormalization is studied for a toy model of a quantum particle moving around a ring, threaded by a magnetic flux $\theta$. Different renormalization group (RG) procedures lead to the same generic RG flow diagram,…
In the study of quantum vacuum energy and the Casimir effect, it is desirable to model the conductor by a potential of the form $V(z)=z^\alpha$. This "soft wall" model was proposed so as to avoid the violation of the principle of virtual…
We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…
In this work we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. As before we utilize the methods, properties, and results obtained by means of classical…
Contour integral representations for Riemann's Zeta function and Dirichelet's Eta (alternating Zeta) function are presented and investigated. These representations flow naturally from methods developed in the 1800's, but somehow they do not…
A previously introduced method to renormalize the one-loop stress tensor and the one-loop vacuum fluctuations in a curved background by a direct local $\zeta$-function approach is checked in some thermal and nonthermal cases. First the…
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…
The paper is devoted to interrelation between the zeta distribution and the Radon transform on the space of $n \times m$ real matrices. We present a self-contained proof of the Fourier transform formula for this distribution. Our method…
We compute one-loop and two-loop beta-functions for vacuum expectation values (VEVs) in gauge theories. In R_xi gauge the VEVs renormalize differently from the respective scalar fields. We focus particularly on the origin and behavior of…
We calculate normalization factors and reflection amplitudes in the W-invariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed…
The Casimir effect describes the attractive force arising due to quantum fluctuations of the vacuum electromagnetic field between closely spaced conducting plates. Traditionally, zeta-regularization is employed in calculations to address…
In this paper we present a method to deal with divergences in perturbation theory using the method of the Zeta regularization, first of all we use the Euler-Mc Laurin Sum formula to associate the divergent integral to a divergent sum in the…
We verify a method which allows to obtain the $\beta$-function of supersymmetric theories regularized by higher covariant derivatives by calculating only specially modified vacuum supergraphs. With the help of this method for a general…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
This paper applies $\zeta$-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…
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…
F. Gygi recently suggested an analytic, norm-conserving, regularized nuclear potential to enable all-electron plane-wave calculations [J. Chem. Theory Comput. 2023, 19, 1300--1309]. This potential $V(r)$ is determined by inverting the…
We study parity violation in $2+1$-dimensional gauge theories coupled to massive fermions. Using the $\zeta$-function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that…
This paper studies the linearized gravitational field in the presence of boundaries. For this purpose, $\zeta$-function regularization is used to perform the mode-by-mode evaluation of BRST-invariant Faddeev-Popov amplitudes in the case of…
Inspired by the results of the Ising model within an imaginary external magnetic field, we introduce a transformation in quantum systems with a theta-vacuum term that amounts to a rescaling of z=cos(theta/2). Making use of this…