This chapter begins the discussion of path integral quantization of Quantum Field Theory (QFT), focusing on the simple case of a real scalar field. Drawing an analogy with quantum mechanics, the vacuum-to-vacuum transition amplitude is defined as the generating functional, which is a functional integral over all field configurations weighted by the exponential of the action. This generating functional is demonstrated to contain all information about the theory. The chapter then establishes the crucial procedure for obtaining n-point correlation functions (Green’s functions) by taking functional derivatives of the generating functional with respect to external sources. The formalism is extended to the complex scalar field, providing a non-canonical, yet systematic, foundation for QFT.

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Path Integrals for Scalar Fields

  • Michael Strickland

摘要

This chapter begins the discussion of path integral quantization of Quantum Field Theory (QFT), focusing on the simple case of a real scalar field. Drawing an analogy with quantum mechanics, the vacuum-to-vacuum transition amplitude is defined as the generating functional, which is a functional integral over all field configurations weighted by the exponential of the action. This generating functional is demonstrated to contain all information about the theory. The chapter then establishes the crucial procedure for obtaining n-point correlation functions (Green’s functions) by taking functional derivatives of the generating functional with respect to external sources. The formalism is extended to the complex scalar field, providing a non-canonical, yet systematic, foundation for QFT.