scholarly journals Scale invariant Euclidean field theory in any dimension

2002 ◽  
Vol 43 (11) ◽  
pp. 5483-5492 ◽  
Author(s):  
Z. Haba
Keyword(s):  
Field Theory ◽  
Scale Invariant ◽  
Euclidean Field ◽  
Euclidean Field Theory

Euclidean field theory

1975 ◽  
Vol 43 (1) ◽  
pp. 41-58 ◽  
Author(s):  
John L. Challifour ◽  
Steven P. Slinker
Keyword(s):  
Field Theory ◽  
Euclidean Field ◽  
Euclidean Field Theory

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.

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