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On the general theory of quantized fields

Technical Report:

Abstract

In my lecture I describe the present stage of the general theory of quantized fields on the example of 5 subjects. They are ordered in the direction from large to small distances. The first one is the by now classical problem of the structure of superselection sectors. It involves the behavior of the theory at spacelike infinity and is directly connected with particle statistics and internal symmetries. It has become popular in recent years by the discovery of a lot of nontrivial models in 2d conformal-field theory, by connections to integrable models and critical behavior in statistical mechanics and by the relations to the Jones` theory of subfactors in von Neumann algebras and to the corresponding geometrical objects (braids, knots, 3d manifolds, ...). At large timelike distances the by far most important feature of quantum field theory is the particle structure. This will be the second subject of my lecture. It follows the technically most involved part which is concerned with the behavior at finite distances. Two aspets, nuclearity which emphasizes the finite density of states in phase space, and the modular structure which relies on the infinite number of degrees of freedom present even locally, and their mutual relations  More>>
Authors:
Fredenhagen, K. [1] 
  1. Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
Publication Date:
Oct 15, 1991
Product Type:
Technical Report
Report Number:
DESY-91-113; CONF-9107201-
Reference Number:
SCA: 662110; PA: DEN-92:000731; SN: 92000645610
Resource Relation:
Conference: 10. IAMP congress on mathematical physics,10. IAMP Kongress ueber Mathematische Physik,Leipzig (Germany), 30 Jul - 9 Aug 1991
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; REVIEWS; PROGRESS REPORT; SUPERSELECTION RULES; SECOND QUANTIZATION; INTERACTION RANGE; CONFORMAL INVARIANCE; SYMMETRY; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS; SMOOTH MANIFOLDS; TOPOLOGY; PARTICLE STRUCTURE; ASYMPTOTIC SOLUTIONS; PHASE SPACE; DEGREES OF FREEDOM; ALGEBRAIC FIELD THEORY; WIGHTMAN FIELD THEORY; FIELD ALGEBRA; ENERGY-LEVEL DENSITY; LOCALITY; GRAVITATIONAL FIELDS; QUANTUM GRAVITY; 662110; THEORY OF FIELDS AND STRINGS
OSTI ID:
10112723
Research Organizations:
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Other: ON: DE92759312; TRN: DE9200731
Submitting Site:
DEN
Size:
20 p.
Announcement Date:
Feb 08, 1992

Technical Report:

Citation Formats

Fredenhagen, K. On the general theory of quantized fields. Germany: N. p., 1991. Web.
Fredenhagen, K. On the general theory of quantized fields. Germany.
Fredenhagen, K. 1991. "On the general theory of quantized fields." Germany.
@misc{etde_10112723,
title = {On the general theory of quantized fields}
author = {Fredenhagen, K.}
abstractNote = {In my lecture I describe the present stage of the general theory of quantized fields on the example of 5 subjects. They are ordered in the direction from large to small distances. The first one is the by now classical problem of the structure of superselection sectors. It involves the behavior of the theory at spacelike infinity and is directly connected with particle statistics and internal symmetries. It has become popular in recent years by the discovery of a lot of nontrivial models in 2d conformal-field theory, by connections to integrable models and critical behavior in statistical mechanics and by the relations to the Jones` theory of subfactors in von Neumann algebras and to the corresponding geometrical objects (braids, knots, 3d manifolds, ...). At large timelike distances the by far most important feature of quantum field theory is the particle structure. This will be the second subject of my lecture. It follows the technically most involved part which is concerned with the behavior at finite distances. Two aspets, nuclearity which emphasizes the finite density of states in phase space, and the modular structure which relies on the infinite number of degrees of freedom present even locally, and their mutual relations will be treated. The next point, involving the structure at infinitesimal distances, is the connection between the Haag-Kastler framework of algebras of local and the framework of Wightman fields. Finally, problems in approaches to quantum gravity will be discussed, as far as they are accessible by the methods of the general theory of quantized fields. (orig.).}
place = {Germany}
year = {1991}
month = {Oct}
}