Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-09-01
Phys.Rev. D53 (1996) 4388-4396
Physics
High Energy Physics
High Energy Physics - Theory
16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effect
Scientific paper
10.1103/PhysRevD.53.4388
The DeWitt expansion of the matrix element $M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle$, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when $x \neq y$ (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing $M_{xy}$ by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of $\tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle$ by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of $\tilde M_{xy}$ as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of $\tilde M_{xy}$ on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.
Dilkes F. A.
McKeon Dennis G. C.
No associations
LandOfFree
Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral 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 Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-341484