Conservation-law violation at high energy by anomalies

Journal Article · Sat Mar 15 04:00:00 EST 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.1591· OSTI ID:5480680

Christ, N H

The time evolution of a quantum Fermi field is investigated in the background of a Minkowski-space, Yang-Mills field configuration with nonvanishing topological charge. The Fermi system is assumed to possess a current j/sub ..mu../(x) conserved up to an axial-vector anomaly: partial/sup ..mu../j/sub ..mu../ = (g/sup 2//32..pi../sup 2/) N/sub i/jF/sup i//sub munu/F/sup j/..mu nu... It is shown explicitly that the time-dependent Yang-Mills field A/sub ..mu../(x,t) creates and destroys fermions in such a way that the total fermionic charge ..integral.. j/sub 0/(x,t) d/sup 3/x present in the final state differs from that in the initial state by precisely the amount predicted by the anomaly equation. If A/sub ..mu../(x,t) approaches a gauge transformation sufficiently rapidly for large t, this change in charge can be identified with the number of zero crossings present in the energy spectrum of the time-dependent Dirac Hamiltonian. Finally, it is demonstrated that the change in the charge carried by the fermions will differ from that predicted by the axial-vector anomaly if the large-time limit of A/sub ..mu../ contains physical radiation.

• Research Organization: Department of Physics, Columbia University, New York, New York 10027
• OSTI ID: 5480680
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645301* -- High Energy Physics-- Particle Invariance Principles & Symmetries-- General-- (-1987)
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYON NUMBER
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EIGENSTATES
ENERGY SPECTRA
EQUATIONS
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
HAMILTONIANS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRICES
MINKOWSKI SPACE
PARTICLE MODELS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
S MATRIX
SPACE
SPECTRA
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
TIME DEPENDENCE
UNIFIED GAUGE MODELS
VACUUM STATES
WARD IDENTITY
WAVE EQUATIONS
WEINBERG-SALAM GAUGE MODEL
YANG-MILLS THEORY