Rules for integrals over products of distributions from coordinate independence of path integrals

@article{Kleinert2000RulesFI,
  title={Rules for integrals over products of distributions from coordinate independence of path integrals},
  author={Hagen Kleinert and A. M. Chervyakov},
  journal={The European Physical Journal C - Particles and Fields},
  year={2000},
  volume={19},
  pages={743-747}
}
Abstract. In perturbative calculations of quantum-mechanical path integrals in curvilinear coordinates, one encounters Feynman diagrams involving multiple temporal integrals over products of distributions which are mathematically undefined. In addition, there are terms proportional to powers of Dirac $ \delta $-functions at the origin coming from the measure of path integration. We derive simple rules for dealing with such singular terms from the natural requirement of coordinate independence… 

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References

SHOWING 1-3 OF 3 REFERENCES

Path Integrals in Quantum Mechanics Statistics and Polymer Physics

Elementary properties and simple solutions external sources, correlation function and perturbation theory semiclassical time displacement amplitude Feynman-Kleinert variational approach and

Introduction to the theory of quantized fields

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