Quantum field theory: the path-integral approach

2018 ◽  
pp. 15-207
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Integral Approach ◽  
Quantum Field ◽  
Path Integral Approach

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 Some comments on infinities on quantum field theory: A functional integral approach

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Luiz C. L. Botelho
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Function Space ◽  
Functional Integral ◽  
Field Theories ◽  
Integral Approach ◽  
Quantum Field ◽  
Functional Integrals ◽  
Euclidean Field ◽  
The Subject

AbstractWe analyze on the formalism of probabilities measures-functional integrals on function space the problem of infinities on Euclidean field theories. We also clarify and generalize our previous published studies on the subject.

scholarly journals Peierls brackets in non-Lagrangian field theory

2014 ◽  
Vol 29 (27) ◽  
pp. 1450157 ◽  
Author(s):  
A. A. Sharapov
Keyword(s):  
Field Theory ◽  
Poisson Bracket ◽  
Path Integral ◽  
Deformation Quantization ◽  
Equations Of Motion ◽  
Integral Approach ◽  
Lagrangian Dynamics ◽  
Path Integral Approach ◽  
Lagrangian Field Theory

The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson bracket on the space of solutions to the classical equations of motion, be they Lagrangian or not. The bracket generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.

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.

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