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Critical Review of Path Integral Formulation

2008/01/13 by Takehisa Fujita, Fujita, Takehisa
Computer Science · Engineering · #Distributed and Parallel Computing Systems #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle Accelerators and Free-Electron Lasers

paper · pdf · doi:10.48550/arxiv.0801.1933

openalex publication_date 2008/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates xn. However, the path integral expression cannot be connected to the dynamics of classical mechanics, even though, superficially, there is some similarity between them. Further, the field theory path integral in terms of many dimensional integrations over fields does not correspond to the field quantization. We clarify the essential difference between Feynman's original formulation of path integral in QED and the modern version of the path integral method prevailing in lattice field theory calculations, and show that the former can make a correct second quantization while the latter cannot quantize fields at all and its physical meaning is unknown.

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