Perturbation theory is the standard method to study quantum field theories in the small coupling regime. However, the interplay of perturbative expansion and the thermodynamic limit remains controversial. In particular, arguments were put forward that the infinite volume limit of perturbative coefficients does not give the correct infinite volume asymptotic perturbation expansion of asymptotica...

in chemical engineering, several processes are represented by singular boundary value problems. in general, classical numerical methods fail to produce good approximations for the singular boundary value problems. in this paper, chebyshev finite difference (chfd) method and dtm-pad´e method, which is a combination of differential transform method (dtm) and pad´e approximant, are applied for sol...

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis of tensor invariants of the curvatures of a gravity and gauge field background, to the second order, is derived, and the form factors acting on them are obt...

Abstract The structure of the QFT expansion is studied in the framework of a new “Causal analytic version” of the perturbation theory. Here, the leading idea is to combine the renormalization group (RG) invariance with a general property of causality expressed in the form of the Q2–analyticity. This combining is performed by a special procedure, “analytization”. The procedure, first proposed in...

1 Expansion in the quark masses and 1/Nc It is generally accepted that QCD possesses an exact U(3)R×U(3)L flavour symmetry in the limitmu=md=ms= 0,Nc→∞. We furthermore assume that (a) the axial part of this symmetry is spontaneously broken and (b) that, in the vicinity of this point, the low energy properties of the theory are governed by the Goldstone bosons associated with this symmetry break...

We study a system of particles with nearest- and next-nearest-neighbor exclusion on the square lattice (hard squares). This system undergoes a transition from a fluid phase at low density to a columnar-ordered phase at high density. We develop a systematic high-activity perturbation expansion for the free energy per site about a state with perfect columnar order. We show that the different term...

Approximate resolution of linear systems of differential equationswith varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from QuantumMechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system....

Based on the special properties of Liouville eigenoperators a perturbation theory for the partition sum is given. It is applicable for any temperature and includes the case of degenerate Hamiltonians. To demonstrate the realibility of the method, the second order correction to the atomic limit grand canonical potential of the Hubbard model is calculated and compared to results known from the li...

The chiral Lagrangian for baryons is formulated in an expansion in 1/Nc. The chiral Lagrangian implements the contracted spin-flavor symmetry of large-Nc baryons as well as nonet symmetry of the leading planar diagrams. Large-Nc consistency conditions ensure that chiral loop corrections are suppressed in 1/Nc through exact cancellation of chiral loop graphs to fixed orders in 1/Nc. Application ...

Perturbative contributions to single-beam two-photon transition rates may be divided into two types. The first, involving low-energy intermediate states, require a high-order perturbation treatment, or an exact diagonalization. The other, involving high-energy intermediate states, only require a low-order perturbation treatment. We show how to partition the effective transition operator into tw...