Application of Tomita-Takesaki theory in algebraic euclidean field theories

Details Application of Tomita-Takesaki theory in algebraic euclidean field theories Application of Tomita-Takesaki theory in algebraic euclidean field theories

1999-12-22

arxiv.org/abs/hep-th/9912219v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages

Scientific paper

The construction of the known interacting quantum field theory models is mostly based on euclidean techniques. The expectation values of interesting quantities are usually given in terms of euclidean correlation functions from which one should be able to extract information about the behavior of the correlation functions of the Minkowskian counterpart. We think that the C*-algebraic approach to euclidean field theory gives an appropriate setup in order to study structural aspects model independently. A previous paper deals with a construction scheme which relates to each euclidean field theory a Poincar\'e covariant quantum field theory model in the sense of R. Haag and D. Kastler. Within the framework of R. Haag and D. Kastler, the physical concept of PCT symmetry and spin and statistics is related to the Tomita-Takesaki theory of von Neumann algebras and this important aspects has been studied by several authors. We express the PCT symmetry in terms of euclidean reflexions and we explicitly identify the corresponding modular operator and the modular conjugation of the related Tomita-Takesaki theory. Locality, wedge duality, and a geometric action of the modular group of the von Neumann algebra of observables, localized within a wedge region in Minkowski space, are direct consequences.

Affiliated with

Also associated with

No associations

Rating

Application of Tomita-Takesaki theory in algebraic euclidean field theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Application of Tomita-Takesaki theory in algebraic euclidean field theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Application of Tomita-Takesaki theory in algebraic euclidean field theories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-519296