Highlight Notes on “Fractional quantum field theory, path integral, and stochastic differential equation for strongly interacting many-particle systems” by Hagen Kleinert

2012 ◽  
Vol 100 (1) ◽  
pp. 10000
Author(s):  
M. Lewenstein
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Path Integral ◽  
Particle Systems ◽  
Quantum Field ◽  
Fractional Quantum ◽  
Strongly Interacting

scholarly journals AN ALGORITHMIC APPROACH TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (03) ◽  
pp. 405-447 ◽  
Author(s):  
MASSIMO DI PIERRO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Gauge Theories ◽  
Quantum Field ◽  
Algorithmic Approach ◽  
Main Emphasis ◽  
Lattice Computation ◽  
Theoretical Foundations ◽  
Minimal Residual

The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper, we review the theoretical foundations and the most basic algorithms required to implement a typical lattice computation, including the Metropolis, the Gibbs sampling, the Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis is on gauge theories with fermions such as QCD. We also provide examples of typical results from lattice QCD computations for quantities of phenomenological interest.

scholarly journals Interparticle potentials in a scalar quantum field theory with a Higgs-like mediating field

2013 ◽  
Vol 91 (4) ◽  
pp. 279-292 ◽  
Author(s):  
Alexander Chigodaev ◽  
Jurij W. Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Equations ◽  
Hamiltonian Formalism ◽  
Particle Systems ◽  
Stationary States ◽  
Quantum Field ◽  
Scalar Theory ◽  
Scalar Quantum ◽  
Interparticle Potentials

We study the interparticle potentials for few-particle systems in a scalar theory with a nonlinear mediating field of the Higgs type. We use the variational method, in a reformulated Hamiltonian formalism of quantum field theory, to derive relativistic three- and four-particle wave equations for stationary states of these systems. We show that the cubic and quartic nonlinear terms modify the attractive Yukawa potentials but do not change the attractive nature of the interaction if the mediating fields are massive.

scholarly journals QUANTIZATION WITHOUT THE WITTEN ANOMALIES

1996 ◽  
Vol 11 (32n33) ◽  
pp. 2601-2609 ◽  
Author(s):  
T.D. KIEU
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Boundary Conditions ◽  
Path Integral ◽  
Quantum Field ◽  
Quantum Fields ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Gauge Transformations ◽  
Gauge Anomalies

It is argued that gauge anomalies are only artefacts of the conventional quantization of quantum field theory. When the Berry’s phase is taken into consideration to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are explicitly shown to be eliminated, without any extra quantum fields introduced.

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.

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