Multiple operator integrals in perturbation theory

Two–loop integrals in chiral perturbation theory

We consider chiral perturbation theory in the meson sector at order E 6. In the terminology of the external field technique, the two–loop graphs so generated are of the sunset type. We discuss the evaluation of several of these in the case where the masses of the particles running in the loops are equal. In particular, we present integral representations that are suitable for the evaluation of ...

Multiple Operator Integrals and Spectral Shift

For a large class of admissible functions f : R 7→ C, the operator derivatives dj dxj f(H0 + xV ), where H0 and V are self-adjoint operators on a separable Hilbert space H, exist and can be represented as multiple operator integrals [1, 14]. Let M be a semi-finite von Neumann algebra acting on H and τ a semi-finite normal faithful trace on M. For H0 = H ∗ 0 affiliated with M and V = V ∗ in the ...

Convenient formulae for some integrals in perturbation theory

The free energy and pressure of a fluid, as given by perturbation theory, involve integrals of the hard sphere correlation functions and their density derivatives. In most applications a straightforward procedure would be to obtain these integrals, possibly numerically, using the formulae and computer codes for the hard sphere correlation functions, given previously [Mol. Phys., 2007, 106, 2; C...

Perturbation Theory for Path Integrals of Stiff Polymers

The wormlike chain model of stiff polymers is a nonlinear σ-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only for periodic and Dirichlet boundary conditions. We modify this theory appropriately and show how to perform a systematic large-stiffness expansions for all physica...

Perturbation theory for Hamiltonian operator matrices and Riccati equations