Three-loop QCD corrections and b-quark decays

We present three-loop (NNNLO) corrections to the heavy-to-heavy quark transitions in the limit of equal initial and final quark masses. In analogy with the previously found NNLO corrections, the bulk of the result is due to the beta_0^2 alpha_s^3 corrections. The remaining genuine three-loop effects for the semileptonic b --> c decays are estimated to increase the decay amplitude by 0.2(2)%. The perturbative series for the heavy-heavy axial current converges very well.Comment: 5 page

General Form of the Color Potential Produced by Color Charges of the Quark

Constant electric charge $e$ satisfies the continuity equation $\partial_\mu j^{\mu}(x)= 0$ where $j^\mu(x)$ is the current density of the electron. However, the Yang-Mills color current density $j^{\mu a}(x)$ of the quark satisfies the equation $D_\mu[A] j^{\mu a}(x)= 0$ which is not a continuity equation ($\partial_\mu j^{\mu a}(x)\neq 0$) which implies that a color charge $q^a(t)$ of the quark is not constant but it is time dependent where $a=1,2,...8$ are color indices. In this paper we derive general form of color potential produced by color charges of the quark. We find that the general form of the color potential produced by the color charges of the quark at rest is given by \Phi^a(x) =A_0^a(t,{\bf x}) =\frac{q^b(t-\frac{r}{c})}{r}\[\frac{{\rm exp}[g\int dr \frac{Q(t-\frac{r}{c})}{r}] -1}{g \int dr \frac{Q(t-\frac{r}{c})}{r}}\]_{ab} where $dr$ integration is an indefinite integration, ~~ $Q_{ab}(\tau_0)=f^{abd}q^d(\tau_0)$, ~~$r=|{\vec x}-{\vec X}(\tau_0)|$, ~~$\tau_0=t-\frac{r}{c}$ is the retarded time, ~~$c$ is the speed of light, ~~${\vec X}(\tau_0)$ is the position of the quark at the retarded time and the repeated color indices $b,d$(=1,2,...8) are summed. For constant color charge $q^a$ we reproduce the Coulomb-like potential $\Phi^a(x)=\frac{q^a}{r}$ which is consistent with the Maxwell theory where constant electric charge $e$ produces the Coulomb potential $\Phi(x)=\frac{e}{r}$.Comment: Final version, two more sections added, 45 pages latex, accepted for publication in JHE

A gauge invariant and string independent fermion correlator in the Schwinger model

We introduce a gauge invariant and string independent two-point fermion correlator which is analyzed in the context of the Schwinger model (QED_2). We also derive an effective infrared worldline action for this correlator, thus enabling the computation of its infrared behavior. Finally, we briefly discuss possible perspectives for the string independent correlator in the QED_3 effective models for the normal state of HTc superconductors.Comment: 14 pages, LaTe

Bosonization in d=2 from finite chiral determinants with a Gauss decomposition

We show how to bosonize two-dimensional non-abelian models using finite chiral determinants calculated from a Gauss decomposition. The calculation is quite straightforward and hardly more involved than for the abelian case. In particular, the counterterm $A\bar A$, which is normally motivated from gauge invariance and then added by hand, appears naturally in this approach.Comment: 4 pages, Revte

Spinons and parafermions in fermion cosets

We introduce a set of gauge invariant fermion fields in fermionic coset models and show that they play a very central role in the description of several Conformal Field Theories (CFT's). In particular we discuss the explicit realization of primaries and their OPE in unitary minimal models, parafermion fields in $Z_k$ CFT's and that of spinon fields in $SU(N)_k, k=1$ Wess-Zumino-Witten models (WZW) theories. The higher level case ($k>1$) will be briefly discussed. Possible applications to QHE systems and spin-ladder systems are addressed.Comment: 6 pages, Latex file. Invited talk at International Seminar dedicated to the memory of D.V.Volkov, Kharkov, January 5-7, 199

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Thirring Model with Non-conserved Chiral Charge

We study the Abelian Thirring Model when the fermionic fields have non-conserved chiral charge: $\Delta {\cal Q}_5 =N$. One of the main features we find for this model is the dependence of the Virasoro central charge on both the Thirring coupling constant and $N$. We show how to evaluate correlation functions and in particular we compute the conformal dimensions for fermions and fermionic bilinears, which depend on the fermionic chiral charge. Finally we build primary fields with arbitrary conformal weight.Comment: pages 1

Generalizations of Yang-Mills Theory with Nonlinear Constitutive Equations

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly.Comment: Submitted to the Proceedings of the 3rd Symposium on Quantum Theory and Symmetries (QTS3) 10-14 September 2003. Preprint 9 pages including reference

Multiflavor Correlation Functions in non-Abelian Gauge Theories at Finite Density in two dimensions

We compute vacuum expectation values of products of fermion bilinears for two-dimensional Quantum Chromodynamics at finite flavored fermion densities. We introduce the chemical potential as an external charge distribution within the path-integral approach and carefully analyse the contribution of different topological sectors to fermion correlators. We show the existence of chiral condensates exhibiting an oscillatory inhomogeneous behavior as a function of a chemical potential matrix. This result is exact and goes in the same direction as the behavior found in QCD_4 within the large N approximation.Comment: 28 pages Latex (3 pages added and other minor changes) to appear in Phys.Rev.

N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also known as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] on the sc and the bcc lattices are extended to order beta^{21} for arbitrary N. The series for the second field derivative of the susceptibility is extended to order beta^{17}. An analysis of the newly computed series for the susceptibility and the (second moment) correlation length yields updated estimates of the critical parameters for various values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values of N, we confirm a good agreement with the present renormalization group estimates. A study of the series for the other observables will appear in a forthcoming paper.Comment: Revised version to appear in Phys. Rev. B Sept. 1997. Revisions include an improved series analysis biased with perturbative values of the scaling correction exponents computed by A. I. Sokolov. Added a reference to estimates of exponents for the Ising Model. Abridged text of 19 pages, latex, no figures, no tables of series coefficient