Partition function (mathematics): Difference between revisions

Revision as of 03:48, 19 September 2019

Revision as of 10:35, 28 November 2019

Line 175:

then partition function can be understood to be a sum or [[Gaussian integral|integral]] over Gaussians. The correlation function <math>C(x_j,x_k)</math> can be understood to be the [[Green's function]] for the differential operator (and generally giving rise to [[Fredholm theory]]). In the quantum field theory setting, such functions are referred to as [[propagator]]s; higher order correlators are called n-point functions; working with them defines the [[effective action]] of a theory.

When the random variables are anti-commuting [[GrassmanGrassmann variablenumber]]s, then the partition function can be expressed as a determinant of the operator ''D''. This is done by writing it as a [[GrassmannBerezin integral]] or(also [[Berezincalled Grassmann integral]]).

==General properties==