Feynman-Diagrammatic Description of the Asymptotics of the Time Evolution Operator in Quantum Mechanics

@article{JohnsonFreyd2010FeynmanDiagrammaticDO,
  title={Feynman-Diagrammatic Description of the Asymptotics of the Time Evolution Operator in Quantum Mechanics},
  author={T. Johnson-Freyd},
  journal={Letters in Mathematical Physics},
  year={2010},
  volume={94},
  pages={123-149}
}
  • T. Johnson-Freyd
  • Published 2010
  • Physics, Mathematics
  • Letters in Mathematical Physics
We describe the “Feynman diagram” approach to nonrelativistic quantum mechanics on $${\mathbb{R}^n}$$, with magnetic and potential terms. In particular, for each classical path γ connecting points q0 and q1 in time t, we define a formal power series Vγ(t, q0, q1) in $${\hbar}$$, given combinatorially by a sum of diagrams that each represent finite-dimensional convergent integrals. We prove that exp(Vγ) satisfies Schrödinger’s equation, and explain in what sense the $${t \to 0}$$ limit… Expand
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