Ricardo Schor

Existence of glueballs in strongly coupled lattice gauge theories

Abstract It is shown that the plaquette-plaquette correlation functions in pure lattice gauge theories exhibit an isolated simple pole in the complex energy variable for large-coupling constants. This implies the existence of isolated one-particle (glueball) states in the space of “boxitons”.

Block renormalization group for Euclidean fermions

Block renormalization group transformations (RGT) for lattice and continuum Euclidean Fermions in d dimensions are developed using Fermionic integrals with exponential and “δ-function” weight functions. For the free field the sequence of actionsDk generated by the RGT from D, the Dirac operator, are shown to have exponential decay; uniform ink, after rescaling to the unit lattice. It is shown that the two-point functionD−1 admits a simple telescopic sum decomposition into fluctuation two-point functions which for the exponential weight RGT have exponential decay. Contrary to RG intuition the sequence of rescaled actions corresponding to the “δ-function” RGT do not have uniform exponential decay and we give examples of initial actions in one dimension where this phenomena occurs for the exponenential weight RGT also.

Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (β≪1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter α=〈s4〉−3〈s2〉2, where 〈sk〉 denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for α>0, β small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.

On the mass spectrum of the

We investigate the mass spectrum of a 2+1 lattice gauge-Higgs quantum field theory with Wilson action βAP+λAH, whereAP(AH) is the gauge (gauge-Higgs) interaction. We determine the complete spectrum exactly for all β, λ>0 by an explicit diagonalization of the gauge invariant “transfer matrix” in the approximation that the interaction terms in the spatial directions are omitted; all gauge invariant eigenfunctions are generated directly. For fixed momentum the energy spectrum is pure point and disjoint simple planar loops and strings are energy eigenfunctions. However, depending on the gauge group and Higgs representations, there are bound state energy eigenfunctions not of this form. The approximate model has a rich particle spectrum with level crossings and we expect that it provides an intuitive picture of the number and location of bound states and resonances in the full model for small β, λ>0. We determine the mass spectrum, obtaining convergent expansions for the first two groups of masses above the vacuum, for small β, λ and confirm our expectations.

2+1

AbstractWe obtain low temperature properties of the classical vector model in a hierarchical formulation in three or more dimensions. We consider the lattice model in a zero or non-zero magnetic field, where the single site spin variable ϕ∈Rv has a density proportional to

Low temperature properties of the hierarchical classical vector model

e^{ - \lambda (\phi ^2 - 1)^2 }

Block averaging renormalization group for lattice and continuum euclidean fermions: Expected and unexpected results

for large λ≦∞. Using renormalization group methods we obtain a convergent expansion for the free energy with zero magnetic field. For non-zero fields a shift formula is used to obtain the effective action generated by the renormalization group transformation (RGT). To obtain the pure state zero field free energy and spontaneous magnetization we take the thermodynamic limit together with the zero field limit at a specified rate. The spontaneous magnetization,m, is calculated, is non-zero and the pure state free energy coincides, as expected, with the zero field free energy. Also the sequence of zero field actions does not have a limit but we show that the sequence of actions generated from the original action shifted bym does; the limiting action corresponds to a non-canonical Gaussian fixed point of the RGT.

Properties of block renormalization group operators for Euclidean fermions in an external gauge field

AbstractWe obtain new properties of d-dimensional lattice ferromagnetic classical N-component vector spin systems in the high temperature region. Each model is characterized by a single site a priori single spin probability distribution (sspd) which we take to be rotationally invariant. Associated with the model is a discrete imaginary time lattice quantum field theory which is known to contain particles of mass m. Letting 〈⋅〉 denote the sspd expectation we show that there exists two bound states below but near the two-particle threshold 2m if, with