Functions and Analysis


An Elementary Primer on Gaussian Integrals

Authors: William O. Straub

Gaussian integrals appear frequently in mathematics and physics, especially probability, statistics and quantum mechanics. One of the truly odd things about these integrals is that they cannot be evaluated in closed form over finite limits but are generally exactly integrable over +/- infinity. Yet their evaluation is still often difficult, particularly multi-dimensional integrals and those involving quadratics, vectors and matrices in the exponential. An added complication is that Gaussian integrals can involve ordinary real or complex variables as well as the less familiar Grassmann variables, which are important in the description of fermions. In this elementary primer we present some of the more common Gaussian integrals of both types, along with methods for their evaluation.

Comments: 9 Pages.

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Submission history

[v1] 2014-04-03 22:36:37

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