Related papers: Fluctuations of quantum fields via zeta function r…
In Part I of this series of papers we have described a general formalism to compute the vacuum effects of a scalar field via local (or global) zeta regularization. In the present Part II we exemplify the general formalism in a number of…
Fluctuations of the electromagnetic field produced by quantized matter in external electric field are investigated. A general expression for the power spectrum of fluctuations is derived within the long-range expansion. It is found that in…
It is shown that the normalized fluctuations of Riemann's zeta zeros around their predicted locations follow the Gaussian law. It is also shown that fluctuations of two zeros, $\gamma _{k}$ and $\gamma _{k+x},$ with $x\sim(\log k)^{\beta}$,…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.
We propose a novel regularization scheme in quantum field theory, denominator regularization (den reg). As simple to apply as dimensional regularization, and similarly compatible with a minimal subtraction renormalization scheme, den reg…
A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum…
The recently introduced second order total generalised variation functional $\mathrm{TGV}_{\beta,\alpha}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $\alpha$ and…
Non-compact symmetries of extended 4d supergravities involve duality rotations of vectors and thus are not manifest off-shell invariances in standard "second-order" formulation. To study how such symmetries are realised in the quantum…
Ihara, Kaneko, and Zagier defined two regularizations of multiple zeta values and proved the regularization theorem that describes the relation between those regularizations. We show that the regularization theorem can be generalized to…
We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the special value at s=1/2. The Euler-characteristic is…
We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…
In this article, I present a volume average regularization for the second functional derivative operator that appears in the metric-basis Wheeler-DeWitt equation. Naively, the second functional derivative operator in the Wheeler-DeWitt…
An alternative point of view to exact renormalization equations is discussed, where quantum fluctuations of a theory are controlled by the bare mass of a particle. The procedure is based on an exact evolution equation for the effective…
We show that regularizing divergent integrals is crucially important when applied to the loop diagrams corresponding to quantum corrections to the coupling of the ``gravitational" scalar field due to the interaction among matter fields. We…
The microscopic theories of quantum gravity related to integrable lattice models can be constructed as special deformations of pure gravity. Each such deformation is defined by a second order differential operator acting on the coupling…
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected…
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…
A quantization method based on replacement of c-number by c-number parameterized by an unbiased hidden random variable is developed. In contrast to canonical quantization, the replacement has straightforward physical interpretation as…
We re-examine results of the Liouville theory and provide arguments that a {\it negative} bare cosmological constant is essential to define two-dimensional quantum gravity. From this we are naturally led to a regularization of quantum…
The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential…