Hopping-parameter expansion and the Schwinger model with Wilson fermions

The hopping-parameter expansion method is used to study the Euclidean lattice Schwinger model with Wilson fermions. The effect of virtual fermion loops is also analyzed. The relation between the \(\bar \psi \psi\) operators in the continuum and on the lattice is constructed. Our result shows satisfactory scaling behavior and reproduces well the exactly calculable value for the fermion condensate in the continuum.     

Conformal-covariant Wilson expansion in perturbation theory

The Wilson expansion at light-like distances is investigated in perturbation theory. Ward identities for broken conformal symmetry are used; it is found that, for any value of the physical coupling constant, the Wilson expansion is asymptotically conformal covariant provided there exists a non-trivial scale-invariant skeleton theory.     

Simulating the all-order hopping expansion II: Wilson fermions

We investigate the extension of the Prokof'ev–Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the two-point function on a finite lattice to arbitrary order. Tests are conducted for a constant background field i.e. free fermions at some mass. For the method introduced here this is expected to be a representative case. Its advantage is that we know the exact answers and can thus make stringent tests on the numerics. The approach is formulated in both two and three space–time dimensions. In D=2$D=2$ Wilson fermions enjoy special positivity properties and the simulation is similarly efficient as in the Ising model. In D=3$D=3$ the method also works at sufficiently large mass, but there is a hard sign problem in the present formulation hindering us to take the continuum limit.     

Randomized Wilson loops,reduced models and the large D expansion

Reduced models are matrix integrals believed to be related to the large N limit of gauge theories. These integrals are known to simplify further when the number of matrices D (corresponding to the number of space–time dimensions in the gauge theory) becomes large. Even though this limit appears to be of little use for computing the standard rectangular Wilson loop (which always singles out two directions out of D), a meaningful large D limit can be defined for a randomized Wilson loop (in which all D directions contribute equally). In this article, a proof-of-concept demonstration of this approach is given for the simplest reduced model (the original Eguchi–Kawai model) and the simplest randomization of the Wilson loop (Brownian sum over random walks). The resulting averaged Wilson loop displays a scale behavior strongly reminiscent of the area law.     

Equivalence of the “Wilson expansion” and a generalized parton model

For a target made with constituents which interact via an asymptotically free theory, it is possible to define some parton densities in the deep inelastic region and at any order of the running coupling constant. These densities depend only on the structure of the target and their Q² dependence is governed by master equations. At first order the result of Altarelli and Parisi is recovered. The scattering of any current off the target is described by a convolution of these parton densities with some charge densities, depending on the couplings of the current to the partons. All those results are equivalent to those of the Wilson operator formalism. Some explicit examples are given.     

NC Wilson lines and the inverse Seiberg-Witten map for non-degenerate star products

Open Wilson lines are known to be the observables of non-commutative gauge theory with Moyal-Weyl *-product. We generalize these objects to more general *-products. As an application we derive a formula for the inverse Seiberg-Witten map for *-products with invertible Poisson structures.Received: 13 February 2004, Revised: 1 March 2004, Published online: 8 April 2004     

Large momentum properties and Wilson short distance expansion in non-perturbative field theory

Large momentum properties and Wilson-Zimmerman short-distance expansion are established via phase-space analysis for the weakly coupled massive Gross-Neveu model in dimension 2. Methods are applicable more generally.     

Short-distance expansion of Wilson loops,gluon condensation and Monte Carlo lattice results

The short-distance expansion of Wilson loops in terms of composite gluon operators (gluon condensate) is studied. The 2-loop perturbative contribution to Wilson loop rations is evaluated. Monte Carlo lattice results for SU(2) gluodynamics are analyzed in terms of this expansion. Consistent results for the gluon condensate are found.     

Regimes of laser plasma expansion at optical breakdown in the normal atmosphere

Propagation regimes of a plasma (fast ionization wave, laser-supported radiation wave, and laser-supported detonation wave) generated by laser radiation in a wide range of intensities (5 × 10⁸?10¹¹ W/cm² ) are described. The regimes were analyzed on the basis of the calculated dependence of the propagation velocity on the laser radiation intensity. The lower bound of the velocity was used for the fast ionization wave. Calculation results agree with experimental data and show that the plasma propagates as a fast ionization wave in the above range of intensities.     

Schur function expansion for normal matrix model and associated discrete matrix models

We consider Schur function expansion for the partition function of the model of normal matrices. This expansion coincides with Takasaki's expansion for tau functions of Toda lattice hierarchy. We show that the partition function of the model of normal matrices is, at the same time, a partition function of certain discrete models, which can be solved by the method of orthogonal polynomials. We obtain discrete versions of various known matrix models: models of non-negative matrices, unitary matrices, normal matrices. We also introduce Hermitian and unitary two-matrix models with generalized interaction terms in continuous and discrete versions.     

On the Taylor expansion of the expression for the transition probability for normal absorption processes

Molecular reorientation of 2-chloropyrimidine dissolved in CS₂ (0·1 M) has been investigated by means of ¹³C and proton relaxation. Although weakly coupled, the proton system subjected to non-selective 180-τ-90 pulse sequences allows the determination of one autocorrelation and one cross-correlation dipolar spectral density. The proton and carbon-13 relaxation data allow the complete determination of the rotational diffusional tensor:

and

It is shown that scalar relaxation due to nitrogen-14, has no effect on proton longitudinal relaxation time, because of a cross term due to the symmetry of the molecule, although this mechanism could, a priori, have been thought to be important. Finally, the nitrogen relaxation time recalculated with D_xx , D_yy , D_zz and the quadrupolar coupling tensor is in agreement with the observed linewidth.     

Effects of the condensation and scattering of radiation at the plasma-dynamic expansion of the detonation products of lead azide

The kinetics of the superluminescence of lead atoms, Pb ³ P ₁ ⁰ → ¹ D ₂ (722.9 nm) and ³ P ₁ ⁰ → ³ P ₂ (405.8 nm), at the fast adiabatic expansion and cooling of the detonation products of lead azide Pb(N₃)₂ in vacuum has been studied. The effects of the condensation and scattering of light from drop clusters in an optically active heterophase medium has been analyzed in order to interpret the experiments in laser detonation plasma-dynamic systems based on metal azides.     

Fourier analysis and Wilson Loops

The quantum average of the Wilson Loop is computed through Fourier analysis of the potentials and functional integration over the coefficients. Simple results are obtained in the abelian case as well as in the N→∞ limit of the nonabelian theory.     

Small-distance-behaviour analysis and Wilson expansions

A previously described method to obtain the asymptotic forms of vertex functions at large momenta is, with the help of Wilson operator product expansion formulas, extended to momenta where the vertex functions of the zero-mass theory underlying the asymptotic forms are infrared singular. To obtain from asymptotic forms information on asymptotic behaviour requires assumptions on the behaviour of the zero-mass theory in the limit of infinite dilatation. One particular set of assumptions is discussed and found to pass a simple consistency test; this set of assumptions leads to power laws, or slight modifications thereof, with coupling-constant-independent exponents. The detailed discussion is given for the ⁴ model.