2009/12/16 by Ulrik M. Svensson, Svensson, Ulrik M. · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Stochastic processes and financial applications #advanced mathematical theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0912.3172
9 pages, 3 figures
arxiv created 2009/12/16 · arxiv updated 2010/01/14
In this paper we present a general formula for the inhomogeneous non-Gaussian integral Id(S1,S2)=∫ dx1... dxd e^-1/2S12-S2, where S1 and S2 are symmetric quadratic forms. The solution depends on the eigenvalues of the matrix A=-iM2M1-1, where M1 and M2 are the matrix representations of S1 and S2 respectively. In the 2-dimensional case we also give a manifestly SO(2)-invariant formulation in terms of invariants of the matrix A. An expression for I(S1,S2) in the infinite-dimensional case is calculated and the solution depends only on the determinants of M1 and M2. The infinite-dimensional case may be of use in QFT.