Unexpected Applications of Hill's Differential Equations in Quantum Field Theory and Cosmology

2003 ◽  
Vol 18 (12) ◽  
pp. 2159-2166
Author(s):  
V. M. Mostepanenko
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
External Field ◽  
Differential Equations ◽  
Parametric Resonance ◽  
Physical Theory ◽  
Pair Creation ◽  
Physical Effect ◽  
Inflationary Cosmology ◽  
Quantum Field

The effect of the exponential pair creation from vacuum by the external field periodic in time is discussed. Two prospective applications of this physical effect in quantum field theory and in inflationary cosmology are considered. Being a nontrivial example of a parametric resonance, the effect of exponential pair creation may serve as an illustration of the effectiveness of mathematics in physical theory.

Electrodynamics

2018 ◽  
Author(s):  
James T. Cushing
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Physical Theory ◽  
Special Theory ◽  
Classical Electrodynamics ◽  
Quantum Field ◽  
Theory Of Relativity ◽  
Electric And Magnetic Fields ◽  
Fundamental Physical

Electric charges interact via the electric and magnetic fields they produce. Electrodynamics is the study of the laws governing these interactions. The phenomena of electricity and of magnetism were once taken to constitute separate subjects. By the beginning of the nineteenth century they were recognized as closely related topics and by the end of that century electromagnetic phenomena had been unified with those of optics. Classical electrodynamics provided the foundation for the special theory of relativity, and its unification with the principles of quantum mechanics has led to modern quantum field theory, arguably our most fundamental physical theory to date.

scholarly journals Path Integral based Non-equilibrium Quantum Field Theory of Non-relativistic Pairs inside an Environment

2021 ◽  
Author(s):  
Tobias Binder
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Equations ◽  
Path Integral ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Einstein Condensation ◽  
Full Potential ◽  
Quantum Field ◽  
Non Equilibrium

Abstract We derive differential equations from path integral based non-equilibrium quantum field theory, that cover the dynamics and spectrum of non-relativistic two-body fields for any environment. For concreteness of the two-body fields, we choose the full potential non-relativistic Quantum Electrodynamics Lagrangian in this work. After closing the correlation function hierarchy of these differential equations and performing consistency checks with previous literature under certain limits, we demonstrate the range of physics applications. This includes Cosmology such as Dark Matter in the primordial plasma, Quarkonia Physics inside a quark-gluon plasma, and Condensed and strongly Correlated Matter Physics such as Bose-Einstein condensation or Superconductivity. Since we always had to take limits or approximations of our equations in order to recover those known cases, our equations could contain new phenomena. In particular they are based on non-equilibrium Green's function that can deal with non-hermite potentials as well as dynamical formation of different extreme phases. We propose a scheme for other Lagrangian based theories or higher N-body states such as molecules to derive analogous equations.

scholarly journals Equilibration in an interacting field theory

2002 ◽  
Vol 80 (9) ◽  
pp. 987-993
Author(s):  
M E Carrington ◽  
R Kobes ◽  
G Kunstatter ◽  
D Pickering ◽  
E Vaz
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Equations ◽  
Thermal Equilibrium ◽  
Distribution Functions ◽  
Coupled Systems ◽  
Quantum Field ◽  
Numerical Techniques ◽  
Different Temperatures ◽  
Integral Differential Equations

We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields that are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we examine the master equations that describe the time evolution of the distribution functions for the two coupled systems. By making a few reasonable assumptions we reduce the resulting coupled integral/differential equations to a pair of differential equations that can be solved numerically relatively easily and which give physically sensible results. PACS No.: 11.10W

Inflation and primordial perturbations

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Large Field ◽  
Inflationary Cosmology ◽  
Small Field ◽  
Quantum Field ◽  
Curved Space ◽  
Slow Roll ◽  
Starobinsky Model ◽  
Single Field

Review of inflationary cosmology. Single-field slow-roll inflation. Large-field inflation and small-field inflation. Starobinsky model. Quantum field theory in curved space. Generation of primordial perturbations during inflation. Mukhanov-Sasaki equation. Scalar and tensor perturbations.

Sign in / Sign up

Export Citation Format

Share Document