Related papers: Vacuum energy for generalised Dirac combs at $T = …
It was long believed that there is a zero-point energy in the form of h\omega/2 for massive particles, which is obtained from Schr\"odinger equation for the harmonic oscillator model. In this paper, it is shown, by the Dirac oscillator,…
We use zeta function techniques to give a finite definition for the Casimir energy of an arbitrary ultrastatic spacetime with or without boundaries. We find that the Casimir energy is intimately related to, but not identical to, the…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
The problem of cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, the vacuum energy is important for the Universe even in the absence of gravity, i.e. in the case when the Newton…
Recently we introduced a new technique for computing the average free energy of a system with quenched randomness. The basic tool of this technique is a distributional zeta-function. The distributional zeta-function is a complex function…
We discuss some controverted aspects of the evaluation of the thermal energy of a scalar field in a one-dimensional compact space. The calculations are carried out using a generalised zeta function approach.
We study the dynamical behaviour of the quantum cellular automaton of Refs. [1, 2], which reproduces the Dirac dynamics in the limit of small wavevectors and masses. We present analytical evaluations along with computer simulations, showing…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
We consider the vacuum energy for a scalar field subject to a frequency dependent boundary condition. The effect of a frequency cut-off is described in terms of an {\it incomplete} $\zeta$-function. The use of the Debye asymptotic expansion…
In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which…
The one-loop effective potential of a thermodynamic fermion loop under constant magnetic field is studied. As expected, it can be interpreted literally as a discretized sum of $(D-2)$-dimensional energy density above the Dirac sea.…
In quantum field theory, the vacuum is a fluctuating medium which behaves as a nonlinear polarizable material. In this article, we perform the first rigorous derivation of the magnetic Euler-Heisenberg effective energy, a nonlinear…
A concept of Kinetic Energy in Quantum Mechanics is analyzed. Kinetic Energy is not zero in many cases where there are no motion and flux. This paradox can be understood, using expansion of the wave function in Fourier integral, that is on…
We consider full phase-space noncommutativity in the Dirac equation, and find that in order to preserve gauge invariance, configuration space noncommutativity must be dropped. The resulting space structure gives rise to a constant magnetic…
We study the contribution to vacuum decay in field theory due to the interaction between the long and short-wavelength modes of the field. The field model considered consists of a scalar field of mass $M$ with a cubic term in the potential.…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regu-larised vacuum energy. The leading order of this expansion is given by a classical formula due to…
We postulate the existence of a self-adjoint operator associated to a system with countably infinite number of degrees of freedom whose spectrum is the sequence of the nontrivial zeros of the Riemann zeta function. We assume that it…
The general thermodynamic analysis of the quantum vacuum, which is based on our knowledge of the vacua in condensed-matter systems, is consistent with the Einstein earlier view on the cosmological constant. In the equilibrium Universes the…
We calculate the \hkks for the \elm field in the background of a dielectric cylinder with non equal speeds of light inside and outside. The coefficient $a_{2}$ whose vanishing makes the vacuum energy of a massless field unique, turns out to…