Quantum noncompact sigma models

Journal Article · Mon Jun 01 04:00:00 EDT 1987 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527496· OSTI ID:6899506

van Holten, J W

Two possible quantization procedures for field theories with noncompact symmetry are discussed: one in a positive-definite Hilbert space with negative-energy states and one in a Hilbert space with indefinite metric and positive-definite energy. The physical interpretation of these alternative procedures is explained in terms of the realization of the noncompact symmetry, which is broken in one case and not in the other. It is shown that in exactly solvable quantum sigma models the noncompact symmetry is broken in the vacuum. Some arguments supporting the general validity of this result are given. It is concluded that in contrast to theories like quantum electrodynamics, the noncompact sigma models are to be quantized in the positive-definite Hilbert space with negative-energy modes.

• Research Organization: NIKHEF-H, P.O. Box 41882, 1009 DB Amsterdam, The Netherlands
• OSTI ID: 6899506
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 28:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
COMMUTATORS
DEGREES OF FREEDOM
DIFFERENTIAL EQUATIONS
ENERGY LEVELS
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FUNCTIONS
GROUND STATES
HAMILTONIANS
HILBERT SPACE
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
RENORMALIZATION
SIGMA MODEL
SPACE
SYMMETRY
SYMMETRY BREAKING