The Matsubara-Fradkin Thermodynamical Quantization of Podolsky Electrodynamics

In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's auxiliary field method to the quantization of the Podolsky electrodynamics in thermodynamic equilibrium. This approach allows us to write consistently the path integral representation for the partition function of gauge theories in a simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write the most general form for the polarization tensor in thermodynamic equilibrium.Comment: Submitted to Physical Review

Self-duality in Generalized Lorentz Superspaces

We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized derivative vector fields on such superspaces are assumed to form a superalgebra. Introducing corresponding gauge potentials and hence covariant derivatives and curvatures, we define generalized self-duality as the Lorentz covariant vanishing of certain irreducible parts of the curvatures.Comment: 6 pages, Late

Hubbard Model with Luscher fermions

First applications of the new algorithm simulating dynamical fermions are reported. The method reproduces previous results obtained with different techniques.Comment: talk presented at the XII International Symposium LATTICE94, Bielefeld, Germany, September 1994, to appear in the Proceedings. 3 pages, LATEX, required Elsevier espcrc2.sty style file is attached at the end of this LATEX text. Postscript figures included in the latex document with the epsf facilit

Charge-Density-Wave and Superconductor Competition in Stripe Phases of High Temperature Superconductors

We discuss the problem of competition between a superconducting (SC) ordered state with a charge density wave (CDW) state in stripe phases of high $T_c$ superconductors. We consider an effective model for each stripe motivated by studies of spin-gapped electronic ladder systems. We analyze the problem of dimensional crossover arising from inter-stripe SC and CDW couplings using non-Abelian bosonization and renormalization group (RG) arguments to derive an effective $O(4)$-symmetric nonlinear $\sigma$-model in $D=2+1$ for the case of when both inter-stripe couplings are of equal magnitude as well as equally RG relevant. By studying the effects of various symmetry lowering perturbations, we determine the structure of the phase diagram and show that, in general, it has a broad regime in which both orders coexist. The quantum and thermal critical behavior is discussed in detail, and the phase coexistence region is found to end at associated $T=0$ as well as $T>0$ tetracritical points. The possible role of hedgehog topological excitations of the theory is considered and argued to be RG irrelevant at the spatially anisotropic higher dimensional low-energy fixed point theory. Our results are also relevant to the case of competing N\'eel and valence bond solid (VBS) orders in quantum magnets on 2D isotropic square as well as rectangular lattices interacting via nearest neighbor Heisenberg exchange interactions.Comment: 9 pages, 3 figures (one with 3 subfigures

Exact Transformation for Spin-Charge Separation of Spin-half Fermions without Constraints

We demonstrate an exact local transformation which maps a purely Fermionic manybody system to a system of spinfull Bosons and spinless Fermions, demonstrating a possible path to a non-Fermi liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a charge-like ``quasicharge'' fermion and a spin-like ``quasispin'' Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U

Theory of the nodal nematic quantum phase transition in superconductors

We study the character of an Ising nematic quantum phase transition (QPT) deep inside a d-wave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N, quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existence of a nematic glass phase in the presence of weak disorder. Some possible implications for cuprate physics are also discussed.Comment: 9 page, 4 figures, an error in one of expressions corrected and a new author was added. New references and footnotes are added and this is the version to appear in PR

Gauge Invariance for Generally Covariant Systems

Previous analyses on the gauge invariance of the action for a generally covariant system are generalized. It is shown that if the action principle is properly improved, there is as much gauge freedom at the endpoints for an arbitrary gauge system as there is for a system with ``internal'' gauge symmetries. The key point is to correctly identify the boundary conditions for the allowed histories and to include the appropriate end-point contribution in the action. The path integral is then discussed. It is proved that by employing the improved action, one can use time-independent canonical gauges even in the case of generally covariant theories. From the point of view of the action and the path integral, there is thus no conceptual difference between general covariance and ``ordinary gauge invariance''. The discussion is illustrated in the case of the point particle, for which various canonical gauges are considered.Comment: 41 pages, ULB-PMIF-92-0