The path integral formulation of Quantum Mechanics is related to Huygens principle, as stated by Feynman in his seminal article [1] and widely commented since then. However Huygens principle does not hold in even dimensions, see this web page for example, or this Physics SE. Can we conclude that path integral only work in odd dimensions then?
[1] Feynman, R. P. (Apr. 1948). “Space-Time Approach to Non-Relativistic Quantum Mechanics”. In: Rev. Mod. Phys. 20 (2), pp. 367–387
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