Analytically reduced form of multicenter integrals from Gaussian transforms

Reduced form for Coulomb-wave multicenter integrals.

Gaussian and Mean Field Approximations for Reduced Yang-Mills Integrals

In this paper, we consider bosonic reduced Yang-Mills integrals by using some approximation schemes, which are a kind of mean field approximation called Gaussian approximation and its improved version. We calculate the free energy and the expectation values of various operators including Polyakov loop and Wilson loop. Our results nicely match to the exact and the numerical results obtained befo...

Gaussian integrals

II.G Gaussian Integrals

It can be reduced to a product of N one dimensional integrals by diagonalizing the matrix K ≡ Ki,j . Since we need only consider symmetric matrices (Ki,j = Kj,i), the eigenvalues are real, and the eigenvectors can be made orthonormal. Let us denote the eigenvectors and eigenvalues of K by q̂ and Kq respectively, i.e. Kq̂ = Kqq̂. The vectors {q̂} form a new coordinate basis in the original N dimensi...

Conditionally Gaussian stochastic integrals

We derive conditional Gaussian type identities of the form E [ exp ( i ∫ T 0 utdBt ) ∣∣∣∣ ∫ T 0 |ut|dt ] = exp ( − 2 ∫ T 0 |ut|dt ) , for Brownian stochastic integrals, under conditions on the process (ut)t∈[0,T ] specified using the Malliavin calculus. This applies in particular to the quadratic Brownian integral ∫ t 0 ABsdBs under the matrix condition A †A2 = 0, using a characterization of Yo...