Fermionization, Convergent Perturbation Theory, and Correlations in the Yang-Mills Quantum Field Theory in Four Dimensions

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function $E(x,y)$ of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as $$E(x,y) \sim |x - y|^{-2 - 2 d_G},$$ \noindent for $|x-y|>>0,$ where $d_G$ is a positive integer depending on the gauge group $G.$ In the case where $G=SU(n),$ we conjecture that $$d_G = {\rm dim}SU(n) - {\rm dim}S(U(n-1) \times U(1)),$$ \noindent so that the rate of decay of correlations increases as $n \to \infty.$Comment: Minor corrections of notation, style and arithmetic errors; correction of minor gap in the proof of Proposition 1.4 (the statement of the Proposition was correct); further remark and references adde

Vitaly Ginzburg and High Temperature Superconductivity: Personal Reminiscences

I offer some personal reminiscences from the period of 1976-1983, when I was a M. Sc. and then a Ph.D. student in Vitaly L. Ginzburg's High Temperature Superconductivity group at the P.N. Lebedev Institute in MoscowComment: To be published in proceedings of the Notre Dame Workshop on the Possibility of Room Temperature Superconductivity, June 2005 v.2: an apposite epigraph adde

Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation

Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton's law with the mass satisfying Einstein's relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the "concentration" assumptions hold for a wide class of rectilinear accelerating motions

Dynamical q-deformation in quantum theory and the stochastic limit

A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q depending on time. After the stochastic (or van Hove) limit, due to the nonlinearity, the atomic and field degrees of freedom become entangled in the sense that the field and the atomic variables no longer commute but give rise to a new algebra with new commutation relations replacing the Boson ones. This new algebra allows to give a simple proof of the fact that the non crossing half-planar diagrams give the dominating contribution in a weak coupling regime and to calculate explicitly the correlations associated to the new algebra. The above results depend crucially on the fact that we do not introduce any dipole or multipole approximation.Comment: Latex, 11 page

Hidden Non-Abelian Gauge Symmetries in Doped Planar Antiferromagnets

We investigate the possibility of hidden non-Abelian Local Phase symmetries in large-U doped planar Hubbard antiferromagnets, believed to simulate the physics of two-dimensional (magnetic) superconductors. We present a spin-charge separation ansatz, appropriate to incorporate holon spin flip, which allows for such a hidden local gauge symmetry to emerge in the effective action. The group is of the form $SU(2)\otimes U_S(1) \otimes U_E(1)$, where SU(2) is a local non-Abelian group associated with the spin degrees of freedom, U_E(1) is that of ordinary electromagnetism, associated with the electric charge of the holes, and U_S(1) is a `statistical' Abelian gauge group pertaining to the fractional statistics of holes on the spatial plane. In a certain regime of the parameters of the model, namely strong U_S(1) and weak SU(2), there is the possibility of dynamical formation of a holon condensate. This leads to a dynamical breaking of $SU(2) \to U(1)$. The resulting Abelian effective theory is closely related to an earlier model proposed as the continuum limit of large-spin planar doped antiferromagnets, which lead to an unconventional scenario for two-dimensional parity-invariant superconductivity.Comment: 32 pages LATEX, one figure. (More details given in the passage from the Hubbard model to the long wavelength lattice gauge theory; one figure added; no changes in the conclusions.

Dual variables for the SU(2) lattice gauge theory at finite temperature

We study the three-dimensional SU(2) lattice gauge theory at finite temperature using an observable which is dual to the Wilson line. This observable displays a behaviour which is the reverse of that seen for the Wilson line. It is non-zero in the confined phase and becomes zero in the deconfined phase. At large distances, it's correlation function falls off exponentially in the deconfined phase and remains non-zero in the confined phase. The dual variable is non-local and has a string attached to it which creates a Z(2) interface in the system. It's correlation function measures the string tension between oppositely oriented Z(2) domains. The construction of this variable can also be made in the four-dimensional theory where it measures the surface tension between oppositely oriented Z(2) domains.Comment: 13 pages, LaTeX, 4 figures are included in the latex fil

On magnetic catalysis in even-flavor QED3

In this paper, we discuss the role of an external magnetic field on the dynamically generated fermion mass in even-flavor QED in three space-time dimensions. Based on some reasonable approximations, we present analytic arguments on the fact that, for weak fields, the magnetically-induced mass increases quadratically with increasing field, while at strong fields one crosses over to a mass scaling logarithmically with the external field. We also confirm this type of scaling behavior through quenched lattice calculations using the non-compact version for the gauge field. Both the zero and finite temperature cases are examined. A preliminary study of the fermion condensate in the presence of magnetic flux tubes on the lattice is also included.Comment: 38 pages latex, 18 figures and a style file (axodraw) incorporated (some clarifying remarks concerning the validity of the approximations made and some references were added correcting an earlier version; no effect on conclusions; version to appear in Phys. Rev. D.

Topological Phase Transition in the ν=2/3\nu=2/3 Quantum Hall Effect

The double layer $\nu=2/3$ fractional quantum Hall system is studied using the edge state formalism and finite-size diagonalization subject to periodic boundary conditions. Transitions between three different ground states are observed as the separation as well as the tunneling between the two layers is varied. Experimental consequences are discussed.Comment: 11 pages, REVTEX v3.0, 7 figure