Conformal covariance, modular structure, and duality for local algebras in free massless quantum field theories

Journal Article · Mon Aug 01 04:00:00 EDT 1988 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(88)90044-9· OSTI ID:6828567

Hislop, P D

The Tomita modular operators and the duality property for the local von Neumann algebras in quantum field models describing free massless particles with arbitrary helicity are studied. It is proved that the representation of the Poincare group in each model extends to a unitary representation of SU(2, 2), a covering group of the conformal group. An irreducible set of ''standard'' linear fields is shown to be covariant with respect to this representation. The von Neumann algebras associated with wedge, double-cone, and lightcone regions generated by these fields are proved to be unitarily equivalent. The modular operators for these algebras are obtained in explicit form using the conformal covariance and the results of Bisognano and Wichmann on the modular structure of the wedge algebras. The modular automorphism groups are implemented by one-parameter groups of conformal transformations. The modular conjugation operators are used to prove the duality property for the double-cone algebras and the timelike duality property for the lightcone algebras. copyright 1988 Academic Press, Inc.

• Research Organization: Mathematics Department, University of California, Irvine, California 92717
• OSTI ID: 6828567
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 185:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRAIC FIELD THEORY
AXIOMATIC FIELD THEORY
CONFORMAL INVARIANCE
DUALITY
ELEMENTARY PARTICLES
FIELD THEORIES
FOCK REPRESENTATION
HELICITY
INVARIANCE PRINCIPLES
LIE GROUPS
MASSLESS PARTICLES
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MINKOWSKI SPACE
PARTICLE MODELS
PARTICLE PROPERTIES
POINCARE GROUPS
QUANTUM FIELD THEORY
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY
SYMMETRY GROUPS
UNIFIED GAUGE MODELS
UNITARY SYMMETRY