Simulating Equilibrium Behavior of Quantum Fields with Time-evolving Classical Fields

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Real Time ◽  
Time Evolution ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Quantum Fields ◽  
Equilibrium Behavior ◽  
Classical Fields

A set of field configurations (replicas) reaches equilibrium of quantum field theory after real-time evolution obeying classical equations of motion.

scholarly journals CAUSAL PERTURBATION THEORY IN TERMS OF RETARDED PRODUCTS, AND A PROOF OF THE ACTION WARD IDENTITY

2004 ◽  
Vol 16 (10) ◽  
pp. 1291-1348 ◽  
Author(s):  
MICHAEL DÜTSCH ◽  
KLAUS FREDENHAGEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Ward Identity ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum ◽  
Local Construction ◽  
Free Parameters ◽  
Classical Fields

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann [42]. In our formalism the entries of the retarded products are local functionals of the off-shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Stora's "Action Ward Identity" [45]. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald [32]. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.

DIRICHLET FORMS IN TERMS OF WHITE NOISE ANALYSIS I: CONSTRUCTION AND QFT EXAMPLES

1989 ◽  
Vol 01 (02n03) ◽  
pp. 291-312 ◽  
Author(s):  
S. ALBEVERIO ◽  
T. HIDA ◽  
J. POTTHOFF ◽  
M. RÖCKNER ◽  
L. STREIT
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
White Noise ◽  
Random Fields ◽  
Noise Analysis ◽  
Dirichlet Forms ◽  
Quantum Field ◽  
Quantum Fields ◽  
White Noise Analysis ◽  
Nikodym Derivative

Random fields are given in terms of measures which (in general) are singular with respect to that of white noise. However, many such measures can be expressed in terms of white noise through a positive generalized functional acting as a generalized Radon-Nikodym derivative. We give criteria for this to be the case and show that these criteria are fulfilled by Schwinger and Wightman functionals of various nontrivial quantum field theory models. Furthermore a number of closability criteria are given and discussed for the Dirichlet forms associated with positive generalized functionals of white noise. In a second paper we apply these results to the construction of Markov and of quantum fields.

scholarly journals Functorial Evolution of Quantum Fields

2021 ◽  
Vol 9 ◽  
Author(s):  
Stefano Gogioso ◽  
Maria E. Stasinou ◽  
Bob Coecke
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cellular Automata ◽  
Quantum Field ◽  
Quantum Fields ◽  
Causal Order ◽  
Algebraic Quantum ◽  
Starting Point ◽  
Algebraic Framework ◽  
Definition Of

We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way from the causal order of events in spacetime, with no direct mention of analysis or topology. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We draw a strong connection to Algebraic Quantum Field Theory (AQFT), using a sheaf-theoretical approach in our definition of spaces of states over regions of spacetime. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata (QCA) from previous literature. Given the extreme flexibility of our constructions, we propose that our framework be used as the starting point for new developments in AQFT, QCA and more generally Quantum Field Theory.

THERMOFIELD DYNAMICS AND e+e- REACTIONS

2011 ◽  
Vol 26 (17) ◽  
pp. 2881-2897 ◽  
Author(s):  
M. CHEKERKER ◽  
M. LADREM ◽  
F. C. KHANNA ◽  
A. E. SANTANA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Real Time ◽  
Finite Temperature ◽  
Quantum Field ◽  
Time Formalism ◽  
Hadronic State ◽  
Real Time Formalism

The thermofield dynamics, a real-time formalism for finite temperature quantum field theory, is used to calculate the rates for e+e- reactions at finite temperature. The results show the role of temperature in defining a hadronic state after the plasma has been cooled down.

REAL-TIME FORMALISM OF THERMOFIELD DYNAMICS AND MATSUBARA APPROACH IN QUANTUM STATISTICAL PHYSICS

1990 ◽  
Vol 05 (26) ◽  
pp. 2183-2188
Author(s):  
A. A. ABRIKOSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Real Time ◽  
Statistical Physics ◽  
Integration Contour ◽  
Quantum Field ◽  
True Vacuum ◽  
Time Formalism ◽  
Quantum Statistical ◽  
Real Time Formalism

When studying thermodynamic properties by means of quantum field theory methods one can deform the Matsubara integration contour in the complex time plane. The deformations are restricted by Hamiltonian singularities which are due to turning on an interaction. One should construct the real-time technique in the true vacuum taking the interaction into account.

scholarly journals Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 43 ◽  
Author(s):  
Akihiro Nishiyama ◽  
Shigenori Tanaka ◽  
Jack A. Tuszynski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Time Evolution ◽  
Central Region ◽  
Quantum Electrodynamics ◽  
Quantum Tunneling ◽  
Evolution Equations ◽  
Open Systems ◽  
Quantum Field ◽  
The Brain

We derive time evolution equations, namely the Klein–Gordon equations for coherent fields and the Kadanoff–Baym equations in quantum electrodynamics (QED) for open systems (with a central region and two reservoirs) as a practical model of quantum field theory of the brain. Next, we introduce a kinetic entropy current and show the H-theorem in the Hartree–Fock approximation with the leading-order (LO) tunneling variable expansion in the 1st order approximation for the gradient expansion. Finally, we find the total conserved energy and the potential energy for time evolution equations in a spatially homogeneous system. We derive the Josephson current due to quantum tunneling between neighbouring regions by starting with the two-particle irreducible effective action technique. As an example of potential applications, we can analyze microtubules coupled to a water battery surrounded by a biochemical energy supply. Our approach can be also applied to the information transfer between two coherent regions via microtubules or that in networks (the central region and the N res reservoirs) with the presence of quantum tunneling.

Sign in / Sign up

Export Citation Format

Share Document