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.
[v1] 2014-04-03 22:36:37
Unique-IP document downloads: 341 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.