Factorization Algebras in Quantum Field Theory

2016 ◽  
Author(s):  
Kevin Costello ◽  
Owen Gwilliam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Factorization Algebras

Factorization Algebras in Quantum Field Theory

2021 ◽  
Author(s):  
Kevin Costello ◽  
Owen Gwilliam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Local Structure ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field ◽  
Essential Information ◽  
Conformal Blocks ◽  
Factorization Algebras

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin–Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.

scholarly journals Relating Nets and Factorization Algebras of Observables: Free Field Theories

2020 ◽  
Vol 373 (1) ◽  
pp. 107-174 ◽  
Author(s):  
Owen Gwilliam ◽  
Kasia Rejzner
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Equations Of Motion ◽  
Free Field ◽  
Intermediate Step ◽  
Quantum Field ◽  
Associative Algebras ◽  
Main Claim ◽  
Algebraic Quantum ◽  
Factorization Algebras

AbstractIn this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous: perturbative algebraic quantum field theory (pAQFT) and the factorization algebras framework developed by Costello and Gwilliam. To make the comparison as explicit as possible, we use the free scalar field as our running example, while giving proofs that apply to any field theory whose equations of motion are Green-hyperbolic (which includes, for instance, free fermions). The main claim is that for such free theories, there is a natural transformation intertwining the two constructions. In fact, both approaches encode equivalent information if one assumes the time-slice axiom. The key technical ingredient is to use time-ordered products as an intermediate step between a net of associative algebras and a factorization algebra.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Some remarks on a deformed quantum field theory

2002 ◽  
Author(s):  
Marco Aurelio Do Rego Monteiro ◽  
V. B. Bezerra ◽  
E. M.F. Curado
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

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