Anomalies in quantum field theory and differential geometry

Technical Report · Tue Apr 01 04:00:00 EST 1986

DOI:https://doi.org/10.2172/6982663· OSTI ID:6982663

Manes, J L

Anomalies in field theory appeared first in perturbative computations involving Feynman diagrams. It is only recently that differential geometric techniques have been used to obtain the form of gauge and gravitational anomalies in a direct and simple way. This is possible because of the topological nature of the anomaly. In the first chapter of this thesis the gauged Wess-Zumino action is constructed by differential geometry methods. After reviewing the relevant techniques, an expression for the action valid in any (even) number of space-time dimensions is obtained. This expression is compared with Witten's result in four dimensions. The link between topology and the anomaly is provided by the appropriate index theorem. The index density is a supersymmetric invariant polynomial from which the anomaly and other related objects can be obtained through the use of the ''descent equations.'' A new proof of the Atiyah-Singer index theorem for the Dirac operator is presented. This proof is based on the use of a WKB approximation to evaluate the supertrace of the kernel for a supersymmetric hamiltonian. The necessary WKB techniques are developed and mechanical systems with bosonic and fermionic degrees of freedom are discussed.

• Research Organization: Lawrence Berkeley Lab., CA (USA); California Univ., Berkeley (USA). Dept. of Physics
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6982663
• Report Number(s): LBL-22304; ON: DE87002545
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACTION INTEGRAL
DIFFERENTIAL GEOMETRY
FIELD THEORIES
FUNCTIONALS
FUNCTIONS
GEOMETRY
HAMILTONIANS
INTEGRALS
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SUPERSYMMETRY
SYMMETRY
TOPOLOGY
WKB APPROXIMATION