Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-08-24
Nucl.Phys. B389 (1993) 53-80
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, harvmac macro, CERN-TH.6512/92, USITP-92-02
Scientific paper
10.1016/0550-3213(93)90285-W
The 1-loop anomalies of a d-dimensional quantum field theory can be computed by evaluating the trace of the regulated path integral jacobian matrix, as shown by Fujikawa. In 1983, Alvarez-Gaum\'e and Witten observed that one can simplify this evaluation by replacing the operators which appear in the regulator and in the jacobian by quantum mechanical operators with the same (anti)commutation relations. By rewriting this quantum mechanical trace as a path integral with periodic boundary conditions for a one-dimensional supersymmetric nonlinear sigma model, they obtained the chiral anomalies for spin 1/2 and 3/2 fields and selfdual antisymmetric tensors in d dimensions. In this article, we treat the case of trace anomalies for spin 0, 1/2 and 1 fields in a gravitational and Yang-Mills background. We do not introduce a supersymmetric sigma model, but keep the original Dirac matrices $\g^\m$ and internal symmetry generators $T^a$ in the path integral. As a result, we get a matrix-valued action. Gauge covariance of the path integral then requires a definition of the exponential of the action by time-ordering. We exponentiate the factors $\sqrt g$ in the path integral measure by using vector ghosts in order to exhibit the cancellation of the sigma model divergences more clearly. We compute the trace anomalies in d=2 and d=4.
Bastianelli Fiorenzo
van Nieuwenhuizen Peter
No associations
LandOfFree
Trace Anomalies from Quantum Mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Trace Anomalies from Quantum Mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trace Anomalies from Quantum Mechanics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-561996