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Line 47: The integral <math display="block"> \int_{-\infty}^{\infty} \exp\left( -{1 \over 2} a x^2 -iJx\right ) dx = \left ( {2\pi \over a } \right ) ^{1\over 2} \exp\left( -{ J^2 \over 2a }\right ) </math> is proportional to the [[Fourier transform]] of the Gaussian where {{mvar\|J}} is the [[conjugate variables\|conjugate variable]] of {{mvar\|x}}.

Common integrals in quantum field theory: Difference between revisions