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

Generating Functional for Gauge Invariant Actions: Examples of Nonrelativistic Gauge Theories

We propose a generating functional for nonrelativistic gauge invariant actions. In particular, we consider actions without the usual magnetic term. Like in the Born-Infeld theory, there is an upper bound to the electric field strength in these gauge theories.Comment: 14 pages, 2 figures; v2: misprints correcte

Electromagnetic response and effective gauge theory of graphene in a magnetic field

The electromagnetic response of graphene in a magnetic field is studied, with particular emphasis on the quantum features of its ground state (vacuum). The graphene vacuum, unlike in conventional quantum Hall systems, is a dielectric medium and carries an appreciable amount of electric and magnetic susceptibilities. The dielectric effect grows rapidly with increasing filling factor nu in such a way that reflects the 'relativistic' Landau-level characteristics of graphene as well as its valley and spin degeneracy. A close look into the dielectric function also reveals that the Coulomb interaction is efficiently screened on the scale of the magnetic length, leading to a prominent reduction of the exciton spectra in graphene. In addition, an effective gauge theory of graphene is constructed out of the response. It is pointed out thereby that the electric susceptibility is generally expressed as a ratio of the Hall conductance to the Landau gap.Comment: 9 pages, 3 figures, revtex, corrected typo

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

Interactions and the Theta Term in One-Dimensional Gapped Systems

We study how the \theta -term is affected by interactions in certain one-dimensional gapped systems that preserve charge-conjugation, parity, and time-reversal invariance. We exploit the relation between the chiral anomaly of a fermionic system and the classical shift symmetry of its bosonized dual. The vacuum expectation value of the dual boson is identified with the value of the \theta -term for the corresponding fermionic system. Two (related) examples illustrate the identification. We first consider the massive Luttinger liquid and find the \theta -term to be insensitive to the strength of the interaction. Next, we study the continuum limit of the Heisenberg XXZ spin-1/2 chain, perturbed by a second nearest-neighbor spin interaction. For a certain range of the XXZ anisotropy, we find that we can tune between two distinct sets of topological phases by varying the second nearest-neighbor coupling. In the first, we find the standard vacua at \theta = 0, \pi, while the second contains vacua that spontaneously break charge-conjugation and parity with fractional \theta / \pi = 1/ 2, 3/2. We also study quantized pumping in both examples following recent work.Comment: 17 pages, harvmac; v.2 typo corrected and slight re-wording

Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids

We study the spontaneous non-magnetic time-reversal symmetry breaking in a two-dimensional Fermi liquid without breaking either the translation symmetry or the U(1) charge symmetry. Assuming that the low-energy physics is described by fermionic quasiparticle excitations, we identified an "emergent" local $U(1)^N$ symmetry in momentum space for an $N$-band model. For a large class of models, including all one-band and two-band models, we found that the time-reversal and chiral symmetry breaking can be described by the $U(1)^N$ gauge theory associated with this emergent local $U(1)^N$ symmetry. This conclusion enables the classification of the time-reversal symmetry-breaking states as types I and II, depending on the type of accompanying spatial symmetry breaking. The properties of each class are studied. In particular, we show that the states breaking both time-reversal and chiral symmetries are described by spontaneously generated Berry phases. We also show examples of the time-reversal symmetry-breaking phases in several different microscopically motivated models and calculate their associated Hall conductance within a mean-field approximation. The fermionic nematic phase with time-reversal symmetry breaking is also presented and the possible realizations in strongly correlated models such as the Emery model are discussed.Comment: 18 pages, 8 figure

Duality between constraints and gauge conditions

It is shown that in the first order gauge theories under some general assumptions gauge conditions can play the role of new local symmetry generators, while the original constraints become gauge fixing terms. It is possible to associate with this new symmetry a second BRST charge and its anticommutator with the original BRST charge is the Hodge operator of the corresponding cohomology complex.Comment: 7 pages, LaTeX, some changes in the BRST sectio

BRST Invariant Higher Derivative Operators in 4D Quantum Gravity based on CFT

We continue the study of physical fields for the background free 4D quantum gravity based on the Riegert-Wess-Zumino action, developed in Phys. Rev. D {\bf 85} (2012) 024028. The background free model is formulated in terms of a certain conformal field theory on M^4 in which conformal symmetry arises as gauge symmetry, namely diffeomorphism invariance. In this paper, we construct the physical field operator corresponding to any integer power of Ricci scalar curvature in the context of the BRST quantization. We also discuss how to define the correlation function and its physical meanings.Comment: 22 pages, minor typo corrected, published versio