Related papers: Zeta-regularized vacuum expectation values
We establish a novel representation of arbitrary Euler-Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve…
This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadratic forms. Such integral operators naturally arise when…
The Argand diagram is used to display some characteristics of the Riemann Zeta function. The zeros of the Zeta function on the complex plane give rise to an infinite sequence of closed loops, all passing through the origin of the diagram.…
We calculate the vacuum expectation values of local fields for the two-parameter family of integrable field theories introduced and studied by Fateev. Using this result we propose an explicit expression for the vacuum expectation values of…
We compute the beta functions for the three gauge couplings of the Standard Model in the minimal subtraction scheme to three loops. We take into account contributions from all sectors of the Standard Model. The calculation is performed…
Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The…
We consider the zeta distributions which are discrete power law distributions that can be interpreted as the counterparts of the continuous Pareto distributions with unit scale. The family of zeta distributions forms a discrete exponential…
Path integral Monte Carlo simulations are applied to study dense atomic hydrogen in the regime where the protons form a Wigner crystal. The interaction of the protons with the degenerate electron gas is modeled by Thomas-Fermi screening,…
We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…
We compute the three loop $\beta$ function of the Wess-Zumino model to motivate implicit regularization (IR) as a consistent and practical momentum-space framework to study supersymmetric quantum field theories. In this framework which…
The treatment of $\gamma_{5}$ in Dimensional Regularization leads to ambiguities in field-theoretic calculations, of which one example is the coefficient of a particular term in the four-loop gauge $\beta$-functions of the Standard Model.…
By using the standard perturbation theory we study the mass as well as $\theta$ parameter dependence of the Seiberg-Witten theory with $SU(2)$ gauge group, supplemented with a $N=1$ supersymmetric as well as a smaller nonsupersymmetric…
In view of various field-theoretic reasons, in the present work, we study the question of if the usual dimensional regularization can be extended to quantum field theories with an ultraviolet cutoff (Poincare-breaking scale) in a way…
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…
At present, the gauge coupling $\beta$-function in the Standard Model (SM) is known up to four-loop order. As most SM calculations, dimensional regularization was employed. Despite its striking success, other regularization schemes have…
A Hermite type formula is introduced and used to study the zeta function over the real and complex n-projective space. This approach allows to compute the residua at the poles and the value at the origin as well as the value of the…
This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a…
We propose a simple realization of a quantum simulator of the Riemann-Hurwitz (RH) \zeta\ function based on a truncation of its Dirichlet representation. We synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property…
The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function…
The finite Dirichlet series from the title are defined by the condition that they vanish at as many initial zeroes of the zeta function as possible. It turned out that such series can produce extremely good approximations to the values of…