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Coordinate Independence of of Quantum-Mechanical Path Integrals
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kleinert, Hagen Chervyakov, Andrey |
| Abstract | In the previous papers [1,2], we have presented a diagrammatic proof of reparametrization invariance of perturbatively defined quantum-mechanical path integrals. The proper perturbative definition of path integrals was shown to require an extension to a functional integral in D spacetime, and a subsequent analytic continuation to D = 1. In Ref. [1] the perturbative calculations were performed in momentum space, where Feynman integrals in a continuous number of dimensions D are known from the prescriptions of ’t Hooft and M. Veltman [3]. In Ref. [2] we have found the same results directly from the Feynman integrals in the 1 − ε-dimensional time space with the help of the Bessel representation of Green functions. The coordinate space calculation is interesting for many applications, for instance, if one wants to obtain the effective action of a field system in curvilinear coordinates, where the kinetic term depends on the dynamic variable. Then one needs rules for performing temporal integrals over Wick contractions of local fields. In this note we want to show that the reparametrization invariance of perturbatively defined quantummechanical path integrals can be obtained in the coordinate space with the help of a simple but quite general arguments based on the inhomogeneous field equation for the Green function, and rules of the partial integration. The prove does not require the calculation of the Feynman integrals separately and remains valid for the functional integrals in an arbitrary space-time dimension D. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://users.physik.fu-berlin.de/~kleinert/kleinert/openarticle.php?id=305 |
| Alternate Webpage(s) | http://cds.cern.ch/record/431512/files/0003095.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Bessel filter Continuation Desoldering Diagram Functional integration Hooft disease Kinetics Matrix regularization Paper Path integral formulation Perturbation theory (quantum mechanics) Polymer Position and momentum space Preparation Quantum harmonic oscillator Quantum mechanics Respiratory Mechanics Rule (guideline) |
| Content Type | Text |
| Resource Type | Article |
