scholarly journals String field theory-inspired algebraic structures in gauge theories

2009 ◽  
Vol 50 (6) ◽  
pp. 063501 ◽  
Author(s):  
Anton M. Zeitlin
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Gauge Theories ◽  
Algebraic Structures

A NOTE ON THE ANTIBRACKET FORMALISM

1990 ◽  
Vol 05 (07) ◽  
pp. 487-494 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Field Theory ◽  
Master Equation ◽  
String Field Theory ◽  
Quantum Correction ◽  
Gauge Theories ◽  
Open String ◽  
Geometric Meaning ◽  
Geometrical Meaning ◽  
Chern Simons

Certain aspects of the antifield-antibracket formalism for quantization of gauge theories are clarified. In particular, we discuss the geometrical meaning of the antifields, the geometric meaning of the antibracket, and the geometric meaning of the operator Δ that appears in the quantum correction to the master equation. Finally, we point out that the antibracket formalism contains most of the ingredients that would be needed to formulate an abstract Chern-Simons Lagrangian, as in open string field theory.

Lecture on SUSY Gauge Theories and Integrable Systems

1997 ◽  
Vol 11 (26n27) ◽  
pp. 3093-3124
Author(s):  
A. Marshakov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Integrable Systems ◽  
Gauge Theories ◽  
Toda Chain ◽  
Quantum Field ◽  
Standard Quantum ◽  
Integrable Equations ◽  
Complex Curves ◽  
Periodic Toda Chain

I consider main features of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential. The example of periodic Toda chain solutions is considered in detail. Recently found exact nonperturbative solutions to [Formula: see text] SUSY gauge theories are formulated using the methods of the theory of integrable systems and where possible the parallels between standard quantum field theory results and solutions to the integrable systems are discussed.

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.

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