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数理解析研究所講究録

The Feynman path Integral Representation of Green Functions of the Position and the Momentum Operators (スペクトル・散乱理論とその周辺)

弥 一ノ瀬

Published May 1, 2001• 0 citations
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The concept of a Fock–Stueckelberg space of quantum states and a procedure of an operator quantization using only Lagrangians (kinematical quantization) are introduced. A propagator operator 𝒦, matrix elements of which are Green’s functions, is used, and an equation of motion for it is derived. We prove that kinematical quantization is an operator (coordinate-free) form of the Feynman quantization technique. The Feynman path integral (FPI) is obtained as a spectral representation of the operator 𝒦 in a coordinate basis. The connection of a representation of commutation relations in this scheme, the domain of integration in FPI, and causality is mentioned.

Journal of Mathematical Physics•Apr 1, 1983•1 citation
Dfinition of the Feynman path integral in the PPP-representation
The concept of a Fock–Stueckelberg space of quantum states and a procedure of an operator quantization using only Lagrangians (kinematical quantization) are introduced. A propagator operator 𝒦, matrix elements of which are Green’s functions, is used, and an equation of motion for it is derived. We prove that kinematical quantization is an operator (coordinate-free) form of the Feynman quantization technique. The Feynman path integral (FPI) is obtained as a spectral representation of the operator 𝒦 in a coordinate basis. The connection of a representation of commutation relations in this scheme, the domain of integration in FPI, and causality is mentioned.