Path Integral Representation of Quantum Field Theory

Chapter
First Online:
Part of the Springer Tracts in Modern Physics book series (STMP, volume 165)

Abstract

In this chapter, we carry out the translation of the results of Chap. 1 on the path integral representation of quantum mechanics to the path integral representation of quantum field theory. The coordinate operator i.e55-1 h (t) of the quantum mechanical system gets demoted to the cnumber indices (x, y, z) at the same level as the time index t. ie55-2 h (t), we have the second-quantized ie55-3(t, x, y, z) in quantum field theory. The necessity of the second-quantization of the field variable ψ(t, x, y, z) originates from the various paradoxes encountered in relativistic quantum mechanics.

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