Related papers: The finite size spectrum of the 2-dimensional O(3)…
We calculate the self-energy of the Delta (1232) resonance in a finite volume, using chiral effective field theory with explicit spin-3/2 fields. The calculations are performed up-to-and-including fourth order in the small scale expansion…
We derive a characterization of the spectrum of the Sinh-Gordon model in terms of certain nonlinear integral equations. There exists a large class of solutions to these equations which allows a continuation between the infrared and the…
An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra…
Based on Lippmann-Schwinger equation approach, we discuss a three-particle system in finite volume. A set of equations which relate the discrete finite-volume energies to the scattering amplitudes are derived under the approximation of the…
We present the coupled nonlinear integral equations (NLIE) governing the finite size effects in N=1 super sine-Gordon model for the vacuum as well as for the excited states. Their infrared limit correctly yields the scattering data of the…
Noncompact SO(1,N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d \geq 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented…
We propose a new model-independent method for determining hadronic resonances from lattice QCD. The formalism is derived from the general principles of unitarity and analyticity, as encoded in the $N/D$ representation of a partial-wave…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
In this article we complete our formalism relating the finite-volume energy spectrum of a scalar quantum field theory to the three-to-three scattering amplitude, ${\cal M}_3$. In previous work we found a quantization condition relating the…
We point out that ignoring nonlinear effects in finite size scaling may lead to errors in estimates of the critical temperature and Binder cumulants. We show that the order of magnitude of these effects can be estimated from data at…
The possibility of production of pulses with scale-invariant properties at presence of fluctuations of parameters of self-oscillatory system with three-dimensional phase space is shown. The system of equations of inertial nonlinearity…
We consider winding number transitions in the two dimensional O(3) non-linear sigma model, modified by a suitable conformal symmetry breaking term. We discuss the general properties of the relevant instanton solutions which dominate the…
Luescher's finite size mass shift formula in a periodic finite volume, involving forward scattering amplitudes in the infinite volume, is revisited for the two stable distinguishable particle system. The generalized mass shift formulae for…
In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a…
We extend our earlier work on the massive $O(N)$ nonlinear sigma model to other observables. We derive expressions at leading order in the large $N$ expansion at all orders in the loop expansion for the decay constant, vacuum expectation…
We consider a two-dimensional sigma-model with discrete icosahedral/dodecahedral symmetry. We present high-precision finite-size numerical results that show that the continuum limit of this model is different from the continuum limit of the…
In this short note, we derive dimension formulas for spaces of Drinfeld cusp forms corresponding to harmonic cocycles invariant under the group $\mathrm{SL}_2(\mathbb{F}_q[t])$ and with values in absolutely irreducible…
Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert…
We calculate the free energy density of the two dimensional O(3) non linear sigma model over a large temperature region. At high temperatures the calculations could be done by perturbation theory whereas in the low temperature regime we…
We introduce the study of nonlinear harmonic forms. These are forms which minimize the $L_2$ energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence results. We…