Reparametrization Invariance of Path Integrals

Abstract

We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the failure of earlier authors to establish reparametrization invariance which led them to introduce, superfluously, a compensating potential depending on the connection of the coordinate system. We show that problems with invariance are absent by defining path integrals as the epsilon-> 0 -limit of 1+ epsilon -dimensional functional integrals.

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re289/preprint.html

References in corpus (1)

• Perturbation Theory for Particle in a Box

Cited by in corpus (29)

• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Worldline Instantons II: The Fluctuation Prefactor
• Worldline formalism in a gravitational background
• Worldline approach to vector and antisymmetric tensor fields
• Dimensional regularization for N=1 susy sigma models and the worldline formalism
• Gravitational corrections to the Euler-Heisenberg Lagrangian
• Superpositions of Probability Distributions
• Effective action for higher spin fields on (A)dS backgrounds
• BRST treatment of zero modes for the worldline formalism in curved space
• Dimensional regularization of nonlinear sigma models on a finite time interval
• Dimensional regularization of the path integral in curved space on an infinite time interval
• Extended SUSY quantum mechanics: transition amplitudes and path integrals
• 6D trace anomalies from quantum mechanical path integrals
• Quantum theories of (p,q)-forms
• Covariant Effective Action for Quantum Particle with Coordinate-Dependent Mass
• Quantum Behavior of Deterministic Systems with Information Loss. Path Integral Approach
• Reparametrization Invariance of Perturbatively Defined Path Integrals. II. Integrating Products of Distributions
• Perturbation Theory for Path Integrals of Stiff Polymers
• Quantum mechanical path integrals in curved spaces and the type-A trace anomaly
• The formal path integral and quantum mechanics
• Simplified Method for Trace Anomaly Calculations in d=6 and d<6
• Photon-graviton mixing in an electromagnetic field
• U(N|M) quantum mechanics on Kaehler manifolds
• Integrals over Products of Distributions from Manifest Coordinate Invariance of Perturbation Expansions of Path Integrals in Curved Space
• Integrals over Products of Distributions and Coordinate Independence of Zero-Temperature Path Integrals
• On the simplified path integral on spheres
• Coordinate Independence of of Quantum-Mechanical Path Integrals
• Fokker-Planck and Langevin Equations from Forward--Backward Path Integral
• Dimensional Regularization for the Particle Transition Amplitude in Curved Space