Chiral Symmetry Versus the Lattice

After mentioning some of the difficulties arising in lattice gauge theory from chiral symmetry, I discuss one of the recent attempts to resolve these issues using fermionic surface states in an extra space-time dimension. This picture can be understood in terms of end states on a simple ladder molecule.Comment: Talk at the meeting "Computer simulations studies in condensed matter physics XIV" Athens, Georgia, Feb. 19-24, 2001. 14 page

Low temperature expansion for the 3-d Ising Model

We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767

Lattice analysis for the energy scale of QCD phenomena

We formulate a new framework in lattice QCD to study the relevant energy scale of QCD phenomena. By considering the Fourier transformation of link variable, we can investigate the intrinsic energy scale of a physical quantity nonperturbatively. This framework is broadly available for all lattice QCD calculations. We apply this framework for the quark-antiquark potential and meson masses in quenched lattice QCD. The gluonic energy scale relevant for the confinement is found to be less than 1 GeV in the Landau or Coulomb gauge.Comment: 4 pages, 4 figure

Monte Carlo Hamiltonian of lattice gauge theory

We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.Comment: "Non-Perturbative Quantum Field Theory: Lattice and Beyond", Guangzhou, China 200

Series expansions without diagrams

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1

Off-diagonal Gluon Mass Generation and Infrared Abelian Dominance in Maximally Abelian Gauge in SU(3) Lattice QCD

In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of off-diagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)_3 \timesU(1)_8 Landau gauge fixing. The Monte Carlo simulation is performed on $16^4$ at $\beta$=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass $M_{\mathrm{off}} \simeq 1.1-1.2\mathrm{GeV}$ in the region of $r =0.3-0.8$fm, and the propagation is limited within a short range, while the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function $e^{-m_{\rm off}r}/r$ with $m_{\rm off} \simeq 1.3-1.4\mathrm{GeV}$ for $r = 0.1- 0.8$ fm. This also indicates that the spectral function of off-diagonal gluons has the negative-value region

Ambiguities in the up quark mass

It has long been known that no physical singularity is encountered as up quark mass is adjusted from small positive to negative values as long as all other quarks remain massive. This is tied to an additive ambiguity in the definition of the quark mass. This calls into question the acceptability of attempts to solve the strong CP problem via a vanishing mass for the lightest quark.Comment: 9 pages, 1 figure. Revision as will appear in Physical Review Letters. Simplified renormalization group discussion and title change requested by PR

Once more about gauge invariance in \phi\to\gamma\pi0\pi0

It is argued that the realization of gauge invariance condition as a consequent of cancellation between the \phi\to\gamma f0\to\gamma\pi0\pi0 resonance contribution and a \phi\to\gamma\pi0\pi0 background one, suggested in Ref. [1], is misleading.Comment: 4 pages, one reference adde

Sum Rules for the Dirac Spectrum of the Schwinger Model

The inverse eigenvalues of the Dirac operator in the Schwinger model satisfy the same Leutwyler-Smilga sum rules as in the case of QCD with one flavor. In this paper we give a microscopic derivation of these sum rules in the sector of arbitrary topological charge. We show that the sum rules can be obtained from the clustering property of the scalar correlation functions. This argument also holds for other theories with a mass gap and broken chiral symmetry such as QCD with one flavor. For QCD with several flavors a modified clustering property is derived from the low energy chiral Lagrangian. We also obtain sum rules for a fixed external gauge field and show their relation with the bosonized version of the Schwinger model. In the sector of topological charge $\nu$ the sum rules are consistent with a shift of the Dirac spectrum away from zero by $\nu/2$ average level spacings. This shift is also required to obtain a nonzero chiral condensate in the massless limit. Finally, we discuss the Dirac spectrum for a closely related two-dimensional theory for which the gauge field action is quadratic in the the gauge fields. This theory of so called random Dirac fermions has been discussed extensively in the context of the quantum Hall effect and d-wave super-conductors.Comment: 41 pages, Late

Measure of the path integral in lattice gauge theory

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U(1) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.Comment: 5 pages, 2 figure