THE PERTURBATIVE APPROACH TO PATH INTEGRALS: A SUCCINCT MATHEMATICAL TREATMENT

@article{Nguyen2016THEPA,
  title={THE PERTURBATIVE APPROACH TO PATH INTEGRALS: A SUCCINCT MATHEMATICAL TREATMENT},
  author={Timothy Nguyen},
  journal={Journal of Mathematical Physics},
  year={2016},
  volume={57},
  pages={092301}
}
  • Timothy Nguyen
  • Published 18 May 2015
  • Mathematics
  • Journal of Mathematical Physics
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick’s theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal parameter irrespective of convergence properties. We establish invariance properties of such a Wick expansion under coordinate changes and the action of a Lie group of symmetries… 
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