Quantization of the self-dual Yang-Mills system: Exchange algebras and local quantum group in four-dimensional quantum field theories

Journal Article · Mon Mar 29 00:00:00 EST 1993 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.70.1916· OSTI ID:6710293

Chau, L; Yamanaka, I ^[1]

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1. Department of Physics, University of California, Davis, California 95616 (United States) Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We have constructed a quantum field theory for the self-dual Yang-Mills system in terms of the group-valued fields [bold [cflx J]]. They satisfy exchange algebras, of which the structure matrices [bold [cflx R]] satisfy Yang-Baxter equations. We show that the fields [bold [cflx J]] form noncommutative vector spaces of a local quantum group and their products at short distances have nontrivial critical exponents. We obtain the quantum Hamiltonian and equations of motion; identify the generators for their symmetries; and construct the affine-Lie-algebra currents, Virasoro-algebra fields, and hierarchies of linear and nonlinear systems.

• OSTI ID: 6710293
• Journal Information: Physical Review Letters; (United States), Vol. 70:13; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
YANG-MILLS THEORY
QUANTIZATION
EQUATIONS OF MOTION
FOUR-DIMENSIONAL CALCULATIONS
LIE GROUPS
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)