Common integrals in quantum field theory: Difference between revisions

Revision as of 23:03, 7 September 2019

Revision as of 04:21, 8 November 2019

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:<math> \int_{-\infty}^{\infty} \exp\left( {1 \over 2} i a x^2 + iJx\right ) dx = \left ( {2\pi i \over a } \right ) ^{1\over 2} \exp\left( { -iJ^2 \over 2a }\right ). </math>

This result is valid as an integration in the complex plane as long as {{mvar|a}} is non-zero and has a semi-positive imaginary part. See [[Fresnel integral]].

==Gaussian integrals in higher dimensions==