Introduction to Integral Discriminants

Details Introduction to Integral Discriminants Introduction to Integral Discriminants

2009-03-16

arxiv.org/abs/0903.2595v1

JHEP 0912:002,2009

Physics

Mathematical Physics

36 pages, 19 figures

Scientific paper

10.1088/1126-6708/2009/12/002

The simplest partition function, associated with homogeneous symmetric forms S of degree r in n variables, is integral discriminant J_{n|r}(S) = \int e^{-S(x_1 ... x_n)} dx_1 ... dx_n. Actually, S-dependence remains the same if e^{-S} in the integrand is substituted by arbitrary function f(S), i.e. integral discriminant is a characteristic of the form S itself, and not of the averaging procedure. The aim of the present paper is to calculate J_{n|r} in a number of non-Gaussian cases. Using Ward identities -- linear differential equations, satisfied by integral discriminants -- we calculate J_{2|3}, J_{2|4}, J_{2|5} and J_{3|3}. In all these examples, integral discriminant appears to be a generalized hypergeometric function. It depends on several SL(n) invariants of S, with essential singularities controlled by the ordinary algebraic discriminant of S.

Affiliated with

Also associated with

No associations

Rating

Introduction to Integral Discriminants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Introduction to Integral Discriminants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Introduction to Integral Discriminants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-223341