We study approximate solutions to the Schrödinger equation iε∂ψt(x)/∂t = H(x,−iε∇x)ψt(x) with the Hamiltonian H the Weyl quantization of the symbol H(q, p) taking values in the space of bounded operators on the Hilbert space Hf of fast “internal” degrees of freedom. By assumption H(q, p) has an isolated energy band. We prove that interband transitions are suppressed to any order in ε. As a cons...

A systematic loop expansion is formulated in terms of full propagators and vertices. It is based on an expansion of the general solution of an exact non-perturbative flow equation.

We study perturbation theory for spin foam models on triangulated manifolds. Starting with any model of this sort, we consider an arbitrary perturbation of the vertex amplitudes, and write the evolution operators of the perturbed model as convergent power series in the coupling constant governing the perturbation. The terms in the power series can be efficiently computed when the unperturbed mo...

Ren-Cang Li University of Texas at Arlington 15.1 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.2 Singular Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-6 15.3 Polar Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-7 15.4 Generalized Eigenvalue Problems . . . . . . . . . . . . . . . . . . . 15-...

The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT, relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, the experimental tests of the foundations of the standard χPT become possible. Emphasize is put on physical aspects rather than on...

Duality is applied to perturbation theory by deriving, given a series solution in a small parameter, the dual one expressed as a series having as a development parameter the inverse of the same parameter considered as large. Clues for a dual simmetry in perturbation theory are given. The method is applied in quantum mechanics to the Rayleigh-Schrödinger perturbation theory and to time-dependent...

After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion–pion scattering to two–loop accuracy. In the pion–nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy–nucleon expansion is used to construct the effective pion...

An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.

We give a brief introduction to chiral perturbation theory in its various settings. We discuss some applications of recent interest including chiral extrapolations for lattice gauge theory.

I present an outline of chiral perturbation theory and discuss some recent developments in the field. Pacs: 11.30.Rd, 12.39.Fe