Privileged Role of the MidPoint Prescription in Path Integrations forConstrained Systems
Abstract
Detailed discussions are made on the path integral formula of Faddeevand Senjanovic for a Ddimensional sphere (S(D) ) as an example ofconstrained systems. We study the operator counterpart resulting fromthe formula in a modelindependent manner. Under these procedures, itis found that only the midpoint (or Weyl) prescription is allowed togive the correct completeness condition in terms of the sphericalharmonics. Thus, contrary to the ordinary situations one must use themidpoint prescription in the path integral formula for constrained systems.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 July 1988
 DOI:
 10.1143/PTP.80.151
 Bibcode:
 1988PThPh..80..151F