Common integrals in quantum field theory: Difference between revisions

Revision as of 06:29, 21 April 2022

Revision as of 00:03, 9 June 2022

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By again completing the square we see that the Fourier transform of a Gaussian is also a Gaussian, but in the conjugate variable. The larger {{mvar|a}} is, the narrower the Gaussian in {{mvar|x}} and the wider the Gaussian in {{mvar|J}}. This is a demonstration of the [[uncertainty principle]].

This integral is also known as the [[Hubbard-StratonovichHubbard–Stratonovich transformation]] used in field theory.

===Integrals with a complex argument of the exponent===