We use an optimised perturbation expansion called the linear δ-expansion to study the phase transition in a Higgs sector with a continuous symmetry and large couplings. Our results show how to use this non-perturbative method successfully for such problems. We also show how to simplify the method without losing any flexibility. Quantum Field Theory has had many successes over the last fifty yea...

The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A(n) of observables...

The concept of chiral symmetry has been of great importance in elementary-particle physics for many years. ' ' In the context of massless quarks and quantum chromodynamics it is, of course, an exact symmetry, and should survive the proof of confinement in some way. It is not surprising, therefore, that immediately after the presentation of the original MIT bag model4 Chodos and Thorn' attempted...

Thanks to a fluctuation dissipation theorem and the mapping to exactly solvable models, much is known for space-dimension d = 1 [1, 2, 3]. In contrast, the case of d ≥ 2 can only be attacked by approximative methods or field-theoretic perturbative expansions. Using the latter, the fixed point structure of the renormalization group flow for d = 2 + ε has been obtained [1, 4, 5]. Two domains can ...

First order perturbation theory for eigenvalues of arbitrary matrices is systematically developed in all its generality with the aid of the Newton diagram, an elementary geometric construction first proposed by Isaac Newton. In its simplest form, a square matrix A with known Jordan canonical form is linearly perturbed to A(ε) = A+ ε B for an arbitrary perturbation matrix B, and one is intereste...

We show that the resonances of a smooth super-exponentially decaying self-adjoint perturbation of the Laplacian in R n ; n 3 odd, determine the Minakshisundaram coeecients d j ; j 2; of the expansion of the regularized heat (wave) trace, provided that there are no negative eigenvalues and zero is not a resonance. We use this to prove the existence of innnitely many resonances for the perturbati...

A formula is proposed for continuing physical correlation functions to non-integer numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is motivated by studying the strong coupling expansion, but the end result makes no reference to any perturbation theory. It is shown that the formula leads to the corr...

For there is always a wrong sign in the mass of graviton in the so-called perturbation expansion approximation of both Minkowski and de Sitter spacetimes, the existence of gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. We try another way to start from the assumption that the gravitational wave equation should be both general covariant and conformal invariant...

The purpose of this article is to study the persistence of solution of a hyperbolic system under small viscous perturbation. Here, the solution of the hyperbolic system is supposed to be periodic: it is a periodic perturbation of a roll-wave. So, it has an infinity of shocks. The proof of the persistence is based on an expansion of the viscous solution and estimates on Green’s functions. Keywor...

The newly developed single trajectory quadrature method is applied to a two-dimensional example. The results based on different versions of new perturbation expansion and the new Green's function deduced from this method are compared to each other, also compared to the result from the traditional perturbation theory. As the first application to higher-dimensional non-separable potential the obt...