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Vacuum decay in de Sitter space is a process of great physical interest, as it allows to rule out cosmological models in the early and current Universe. Its rate may be described in terms of an instanton in Euclidean space called bounce and…
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We…
We reformulate the problem of the cancellation of the ultraviolet divergencies of the vacuum energy, particularly important at the cosmological level, in terms of a saturation of spectral function sum rules which leads to a set of…
The effective Hamiltonian describing resonant interaction of an ensemble of identical quantum particles with a photon-free vacuum electromagnetic field has been obtained with allowance for the second-order terms over the coupling constant…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
A fundamental tenet of quantum mechanics is that measurements change a system's wavefunction to that most consistent with the measurement outcome, even if no observer is present. Weak measurements produce only limited information about the…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
We calculate the Green's functions for the particle-vortex system, for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field. These Green's functions which describe scattering or bound states (depending…
One of the most efficient methods to obtain the vacuum expectation values for the physical observables in the Casimir effect is based on the using the Abel-Plana summation formula. This allows to derive the regularized quantities by…
In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in…
We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a p-summability condition and for integration of functions from Lebesgue…
We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.
For special kinematic configurations involving a single momentum scale, certain standard relations, originating from the Slavnov-Taylor identities of the theory, may be interpreted as ordinary differential equations for the ``kinetic term''…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
We exploit some properties of the Hurwitz zeta function $\zeta (n,x)$ in order to study sums of the form $\frac{1}{\pi ^{n}}\sum_{j=-\infty}^{\infty}1/(jk+l)^{n}$ and $\frac{1}{\pi ^{n}}\sum_{j=-\infty}^{\infty}(-1)^{j}/(jk+l)^{n}$ for $%…
By using the generalized Abel-Plana formula, we derive a summation formula for the series over the zeros of a combination of the associated Legendre functions with respect to the degree. The summation formula for the series over the zeros…
We present an improved version of Berry's ansatz able to incorporate exactly the existence of boundaries and the correct normalization of the eigenfunction into an ensemble of random waves. We then reformulate the Random Wave conjecture…
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…
We derive the analogue of the vanishing of the cosmological constant in 3+1 dimensions, T_0^0 = 0, in terms of an integral over components of the energy-momentum tensor of a 4+1 dimensional universe with parallel three-branes, and an…
We consider the covariant formulation of the kaon mixing in the context of the propagator method. It results important to check the possibility of a sizable effect in the vacuum regeneration of kaons. We discuss all those terms which may…