Related papers: Riemann zeta zeros and zero-point energy
The vacuum energy density (Casimir energy) corresponding to a massless scalar quantum field living in different universes (mainly no-boundary ones), in several dimensions, is calculated. Hawking's zeta function regularization procedure…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
Global mapping properties of the Riemann Zeta function are used to investigate its non trivial zeros.
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective the renormalization prescriptions not only imply the renormalization of the couplings of the theory in…
The effective one-loop potential on $R^{m+1}\times S^N$ spaces for massless tensor fields is evaluated. The Casimir energy is given as a value of $\zeta-$ function by means of which regularization is made. In even- dimensional spaces the…
We prove a general result on representing the Riemann zeta function as a convergent infinite series in a complex vertical strip containing the critical line. We use this result to re-derive known expansions as well as to discover new series…
The consistent form of the gauge anomaly is worked out at first order in $\theta$ for the noncommutative three-point function of the ordinary gauge field of certain noncommutative chiral gauge theories defined by means of the Seiberg-Witten…
In the paper the well known Riemann Hypothesis is proven. The proof is based on uniform approximation of the zeta function discs of the critical strip placed to the right from the critical line.The basic moment is a use of a new mesure…
We discuss a possible spectral realization of the Riemann zeros based on the Hamiltonian $H = xp$ perturbed by a term that depends on two potentials, which are related to the Berry-Keating semiclassical constraints. We find perturbatively…
The energy composition of the Universe, as emerged from the Type Ia supernova observations and the WMAP data, looks preposterously complex, -- but only at the first glance. In fact, its structure proves to be simple and regular. An analysis…
A fresh approach to the long debated question is proposed, starting from the GRAM-BACKLUND analytical continuation of the Zeta function (G-B Zeta expression). Consideration is given to the symmetric (even-exponent) and anti-symmetric (odd…
We propose a simple fixed point scenario in the renormalization flow of a scalar dilaton coupled to gravity. This would render gravity non-perturbatively renormalizable and thus constitute a viable theory of quantum gravity. On the fixed…
In 1999 Berry and Keating showed that a regularization of the 1D classical Hamiltonian H = xp gives semiclassically the smooth counting function of the Riemann zeros. In this paper we first generalize this result by considering a phase…
Using the zeta function regularization method we calculate the ground state energy of scalar massive field inside a spherical region in the space-time of a point-like global monopole. Two cases are investigated: (i) We calculate the Casimir…
The response of vacuum to the presence of external conditions is the subject of this work. We consider a generalization of the Casimir effect in the presence of curved boundaries on which a sharp potential is concentrated. The profile of…
The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time \R$\times \S^2/\Gamma$ where $\Gamma$ is a finite subgroup of O(3) acting with fixed points. The energy vanishes when $\Gamma$ is…
A quantum-field model of the conformally flat space is formulated using a standard field-theoretical technique, a probability interpretation and a way to establish the classical limit. The starting point is the following: after conformal…
In this paper, we present a proof of the Riemann hypothesis. We show that zeros of the Riemann zeta function should be on the line with the real value 1/2, in the region where the real part of complex variable is between 0 and 1.
We consider a massive scalar field living on the recently found exact quantum space-time corresponding to vacuum spherically symmetric loop quantum gravity. The discreteness of the quantum space time naturally regularizes the scalar field,…