Bose field theory as classical statistical mechanics. III. The classical ising approximation

2007 ◽  
pp. 290-297
Author(s):  
Barry Simon
Keyword(s):  
Field Theory ◽  
Statistical Mechanics ◽  
Classical Statistical Mechanics

scholarly journals FROM EUCLIDEAN FIELD THEORY TO QUANTUM FIELD THEORY

1999 ◽  
Vol 11 (09) ◽  
pp. 1151-1178 ◽  
Author(s):  
DIRK SCHLINGEMANN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Statistical Mechanics ◽  
Quantum Field ◽  
Bounded Operators ◽  
Algebraic Version ◽  
Classical Statistical Mechanics ◽  
Euclidean Field ◽  
Euclidean Field Theory ◽  
Reconstruction Theorem

In order to construct examples for interacting quantum field theory models, the methods of Euclidean field theory turned out to be powerful tools since they make use of the techniques of classical statistical mechanics. Starting from an appropriate set of Euclidean n-point functions (Schwinger distributions), a Wightman theory can be reconstructed by an application of the famous Osterwalder–Schrader reconstruction theorem. This procedure (Wick rotation), which relates classical statistical mechanics and quantum field theory, is, however, somewhat subtle. It relies on the analytic properties of the Euclidean n-point functions. We shall present here a C*-algebraic version of the Osterwalder–Schrader reconstruction theorem. We shall see that, via our reconstruction scheme, a Haag–Kastler net of bounded operators can directly be reconstructed. Our considerations also include objects, like Wilson loop variables, which are not point-like localized objects like distributions. This point of view may also be helpful for constructing gauge theories.

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".  

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