A COMPACT ANALYTICAL APPROXIMATION FOR THE FEYNMAN PROPAGATOR IN CURVED SPACE-TIME

Sep, 1982
25 pages
Published in:
  • Phys.Rev.D 28 (1983) 265
Report number:
  • Print-83-0035 (IAS,PRINCETON)

Citations per year

19841993200220112018102
Abstract: (APS)
In a recent paper, Bekenstein and Parker obtain an approximate formula for the Feynman propagator of a scalar particle traveling in a background gravitational field. They expand a path-integral representation in small fluctuations about a classical path, keeping terms up to quadratic in the fluctuations. Using a Fourier-series technique, they obtain a formula for the quadratic terms as a determinant of an infinite-dimensional matrix. Using an alternative technique, I express the quadratic terms as the determinant of a finite-dimensional, 4×4 matrix. An intuitively appealing geometrical interpretation of the quadratic terms is given. The present technique allows one to prove a conjecture made by Bekenstein and Parker, that the quadratic terms are given by the Van Vleck-Morette determinant whenever the classical path is a geodesic of the background gravitational field.
  • FIELD THEORY: SPACE-TIME
  • PROPAGATOR
  • FIELD THEORY: SCALAR
  • MATHEMATICAL METHODS