Nonperturbative study of the two-frequency sine-Gordon model

The two-frequency sine-Gordon model is examined. The focus is mainly on the case when the ratio of the frequencies is 1/2, given the recent interest in the literature. We discuss the model both in a perturbative (form factor perturbation theory) and a nonperturbative (truncated conformal space approach) framework, and give particular attention to a phase transition conjectured earlier by Delfino and Mussardo. We give substantial evidence that the transition is of second order and that it is in the Ising universality class. Furthermore, we check the UV-IR operator correspondence and conjecture the phase diagram of the theory.Comment: Minor corrections, LaTeX2e, 39 pages, 26 figures (4 pslatex, 1 postscript and 21 eps

Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms

The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with models relevant for particle physics. It is important to understand these finite size corrections as they present a potentially dangerous source of systematic errors for the determination of matrix elements and resonance widths.Comment: 26 pages, 13 eps figures, LaTeX2e fil

Finite size effects in quantum field theories with boundary from scattering data

We derive a relation between leading finite size corrections for a 1+1 dimensional quantum field theory on a strip and scattering data, which is very similar in spirit to the approach pioneered by Luscher for periodic boundary conditions. The consistency of the results is tested both analytically and numerically using thermodynamic Bethe Ansatz, Destri-de Vega nonlinear integral equation and classical field theory techniques. We present strong evidence that the relation between the boundary state and the reflection factor one-particle couplings, noticed earlier by Dorey et al. in the case of the Lee-Yang model extends to any boundary quantum field theory in 1+1 dimensions.Comment: 24 pages, 1 eps figure. Clarifying comments and a reference adde

Casimir effect in the boundary state formalism

Casimir effect in the planar setting is described using the boundary state formalism, for general partially reflecting boundaries. It is expressed in terms of the low-energy degrees of freedom, which provides a large distance expansion valid for general interacting field theories provided there is a non-vanishing mass gap. The expansion is written in terms of the scattering amplitudes, and needs no ultraviolet renormalization. We also discuss the case when the quantum field has a nontrivial vacuum configuration.Comment: 11 pages. Proceedings contribution of talk given at the Workshop on Quantum Field Theory under the Influence of External Conditions (QFEXT07), University of Leipzig, September 16-21, 2007. To appear in J. Phys.

Casimir force between planes as a boundary finite size effect

The ground state energy of a boundary quantum field theory is derived in planar geometry in D+1 dimensional spacetime. It provides a universal expression for the Casimir energy which exhibits its dependence on the boundary conditions via the reflection amplitudes of the low energy particle excitations. We demonstrate the easy and straightforward applicability of the general expression by analyzing the free scalar field with Robin boundary condition and by rederiving the most important results available in the literature for this geometry.Comment: 10 pages, 2 eps figures, LaTeX2e file. v2: A reference is added, some minor modifications made to clarify the text. v3: 9 pages, 3 eps figures, LaTeX2e file, revtex style. Paper throughly restructured and rewritten. Much more details are given, but essential results and conclusions are unchanged. Version accepted for publicatio