Vacuum effects in a spatially homogeneous and isotropic cosmological background

1992 ◽  
Vol 70 (2-3) ◽  
pp. 143-147
Author(s):  
Victor M. Villalba ◽  
Umberto Percoco
Keyword(s):  
Separation Of Variables ◽  
Particle Creation ◽  
Coupling Constant ◽  
Positive Cosmological Constant ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Dimensionless Coupling ◽  
Spatially Homogeneous ◽  
Dimensionless Coupling Constant ◽  
Vacuum Effects

In this article we obtain, by separation of variables, an exact solution to the Klein–Gordon and Dirac equations in a cosmological, spatially-closed, Robertson–Walker space-time with a positive cosmological constant Λ. The model is associated with a universe filled with radiation. We analyze the phenomenon of particle creation for different values of the dimensionless coupling constant ξ.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

scholarly journals Dynamics and the emergence of geometry in an information mesh

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Philip Tee
Keyword(s):  
Ground State ◽  
Quantum Particle ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Graph Properties ◽  
Graph Theoretical Approach ◽  
Dimensionless Coupling ◽  
Dimensionless Coupling Constant ◽  
Ground State Geometry ◽  
The Continuum

Abstract The idea of a graph theoretical approach to modeling the emergence of a quantized geometry and consequently spacetime, has been proposed previously, but not well studied. In most approaches the focus has been upon how to generate a spacetime that possesses properties that would be desirable at the continuum limit, and the question of how to model matter and its dynamics has not been directly addressed. Recent advances in network science have yielded new approaches to the mechanism by which spacetime can emerge as the ground state of a simple Hamiltonian, based upon a multi-dimensional Ising model with one dimensionless coupling constant. Extensions to this model have been proposed that improve the ground state geometry, but they require additional coupling constants. In this paper we conduct an extensive exploration of the graph properties of the ground states of these models, and a simplification requiring only one coupling constant. We demonstrate that the simplification is effective at producing an acceptable ground state. Moreover we propose a scheme for the inclusion of matter and dynamics as excitations above the ground state of the simplified Hamiltonian. Intriguingly, enforcing locality has the consequence of reproducing the free non-relativistic dynamics of a quantum particle.

scholarly journals Energy-momentum of the Friedmann models in General Relativity and the teleparallel theory of gravity

2008 ◽  
Vol 86 (11) ◽  
pp. 1297-1302 ◽  
Author(s):  
M Sharif ◽  
M Jamil Amir
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Spherical Shell ◽  
Momentum Density ◽  
Friedmann Universe ◽  
Coupling Constant ◽  
Dimensionless Coupling ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Dimensionless Coupling Constant

This paper is devoted to the evaluation of the energy-momentum density components for the Friedmann models. For this purpose, we have used Møller’s pseudotensor prescription in General Relativity and a certain energy-momentum density developed from Møller’s teleparallel formulation. We show that the energy density of the closed Friedmann universe vanishes on the spherical shell at the radius ρ = 2[Formula: see text]. This coincides with the earlier results available in the literature. We also discuss the energy of the flat and open models. A comparison shows a partial consistency between Møller’s pseudotensor for General Relativity and teleparallel theory. Further, we show that the results are independent of the free dimensionless coupling constant of the teleparallel gravity.PACS No.: 04.20.–q

BLACK HOLES AND SOLITONS OF THE NONLINEAR ISOVECTOR MODEL

2006 ◽  
Vol 21 (21) ◽  
pp. 4343-4354 ◽  
Author(s):  
NEMATOLLAH RIAZI ◽  
HASSAN NIAD ◽  
SEYED HOSSEIN HENDI
Keyword(s):  
Strong Coupling ◽  
Asymptotic Form ◽  
Flat Space ◽  
Strong Coupling Regime ◽  
Spherically Symmetric ◽  
Coupling Constant ◽  
Curved Space ◽  
Dimensionless Coupling ◽  
Dimensionless Coupling Constant ◽  
Black Hole Solutions

We formulate the nonlinear isovector model in a curved background and calculate the spherically symmetric solutions for weak and strong coupling regimes. The question whether gravity has appreciable effects on the structure of solitons will be examined, in the framework of the calculated solutions, by comparing the flat-space and curved-space solutions. It turns out that in the strong coupling regime, gravity has essential effects on the solutions. It is also shown that the asymptotic form of the metric conforms with that of the charged Reissner–Nordstrom metric. The dimensionless coupling constant of the model has a limit, beyond which a horizon appears in the solutions, indicating the presence of black hole solutions.

scholarly journals QUANTUM GRAVITY IN PLEBANSKI FORMULATION

2011 ◽  
Vol 26 (31) ◽  
pp. 2323-2333
Author(s):  
L. V. LAPERASHVILI
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Gravitational Interaction ◽  
Graviton Mass ◽  
Coupling Constant ◽  
Independent Variables ◽  
Dimensionless Coupling ◽  
Theory Of Gravity ◽  
Dimensionless Coupling Constant ◽  
Nonperturbative Theory

We present a theory of four-dimensional quantum gravity with massive gravitons which may be essentially renormalizable. In Plebanski formulation of general relativity in which the tetrads, the connection and the curvature are all independent variables (and the usual relations among these quantities are valid only on-shell), we consider the nonperturbative theory of gravity with a nonzero background connection. We predict a tiny value of the graviton mass: mg≈1.5×10-42 GeV and extremely small dimensionless coupling constant of the perturbative gravitational interaction: g~10-60. We put forward the idea by Isimori56 on renormalizability of quantum gravity having multi-gravitons with masses m0, m1, …, mN-1.

Separation of variables for the Klein–Gordon and Dirac equations in two-dimensional space-times with a null coordinate

1990 ◽  
Vol 68 (11) ◽  
pp. 1243-1246
Author(s):  
Victor M. Villalba
Keyword(s):  
Dimensional Space ◽  
Separation Of Variables ◽  
Constant Electric Field ◽  
Coordinate Systems ◽  
Constant Acceleration ◽  
Quantum Distribution ◽  
Dirac Equations ◽  
Curvilinear Coordinate ◽  
Klein Gordon ◽  
Free Case

The separation of variables for the Klein–Gordon and Dirac equations, in the presence of electromagnetic fields, for a class of curvilinear coordinate systems with a null coordinate is presented. We show that these coordinates can be associated with a system with constant acceleration. Exact solutions for the free case and for a particle in a constant electric field are obtained. Finally, the quantum distribution of scalar massless particles in the accelerated frame of reference is computed.

scholarly journals QUANTUM SINGULARITIES IN STATIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 729-743 ◽  
Author(s):  
JOÃO PAULO M. PITELLI ◽  
PATRICIO S. LETELIER
Keyword(s):  
Quantum Mechanics ◽  
Wave Operator ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Mathematical Framework ◽  
Physical Content ◽  
Dirac Equations ◽  
Quantum Particles ◽  
Klein Gordon ◽  
Quantum Singularities

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.

scholarly journals ON THE CREATION OF SCALAR PARTICLES IN A FLAT ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 26 (35) ◽  
pp. 2639-2651 ◽  
Author(s):  
S. HAOUAT ◽  
R. CHEKIREB
Keyword(s):  
Exact Solutions ◽  
Effective Action ◽  
Gordon Equation ◽  
Transition Probability ◽  
Particle Creation ◽  
Pair Creation ◽  
Bogoliubov Transformation ◽  
Scalar Particles ◽  
Klein Gordon ◽  
Klein Gordon Equation

The problem of particle creation from vacuum in a flat Robertson–Walker spacetime is studied. Two sets of exact solutions for the Klein–Gordon equation are given when the scale factor is a2(η) = a+b tanh(λη)+c tanh2 (λη). Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. Some particular cosmological models such as radiation dominated universe and Milne universe are discussed. For both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.

Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

Sign in / Sign up

Export Citation Format

Share Document