Chern Simons Electrodynamics Research Articles

Induced curvature effects in Maxwell’s equations

We have studied in this work extended electrodynamics with a relaxed Lorenz gauge condition. We then compare it with the electrodynamics in curved space–time. Interestingly, the interaction of the electromagnetic field with the space curvature induces electric and magnetic charges and currents. The coupling of the electromagnetic field with the particle charge gives rise to its spin. Two spins are found to emerge in addition to their associated helicities. The electromagnetic field is found to be coupled to curvature through its electric and magnetic spins. The electrodynamics in curved space is found to be analogous to massive electrodynamics. When the electromagnetic field travels in curved space–time, it acquires mass depending on the strength of the space curvature. In curved space, the space in which the electromagnetic field travels got an effective electric conductivity proportional to the temporal variation of the metric determinant. The curved space appears to behave like a conducting medium with variable electric conductivity. Moreover, an additional current perpendicular to the magnetic field is induced whenever the space is curved. Axion and Chern–Simons electrodynamics are found to be connected to massive electrodynamics and standard electrodynamics in curved space–time.

Effective theories and non-minimal couplings in low-dimensional systems

Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy–Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields. Next, we establish some comparisons and analyze particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell–Chern–Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.

Chiral magnetic effect and Maxwell–Chern–Simons electrodynamics in Weyl semimetals

The Weyl semimetal, due to a non-zero energy difference in the pair of Weyl nodes, shows chiral magnetic effect (CME). This leads to a flow of dissipationless electric current along an applied magnetic field. Such a chiral magnetic effect in Weyl semimetals has been studied using the laws of classical electrodynamics. It has been shown that the CME in such a semimetal changes the properties namely, frequency-dependent skin depth, capacitive transport, plasma frequency, etc., in an unconventional way as compared to the conventional metals. In the low-frequency regime, the properties are controlled by a natural length scale due to CME called the chiral magnetic length. Furthermore, unlike the conventional metals, the plasma frequency in this case is shown to be strongly magnetic field-dependent. Since the plasma frequency lies below the optical frequency, the Weyl semimetals will look transparent. Such new and novel observations might help in exploiting these class of materials in potential applications which would completely change the future technology.

Induced Maxwell\u2013Chern\u2013Simons effective action in very special relativity

In this paper, we study the one-loop induced photon’s effective action in the very special relativity electrodynamics in (2+1) spacetime (hbox {VSR}–hbox {QED}_{3}). Due to the presence of new nonlocal couplings resulting from the VSR gauge symmetry, we have additional graphs contributing to the langle AArangle and langle AAA rangle amplitudes. From these contributions, we discuss the VSR generalization of the Abelian Maxwell–Chern–Simons Lagrangian, consisting in the dynamical part and the Chern–Simons-like self-couplings, respectively. We use the VSR–Chern–Simons electrodynamics to discuss some non-Ohmic behavior on topological materials, in particular VSR effects on Hall’s conductivity. In the dynamical part of the effective action, we observe the presence of a UV/IR mixing, due to the entanglement of the VSR nonlocal effects to the quantum higher-derivative terms. Furthermore, in the self-coupling aspect, we verify the validity of the Furry’s theorem in the {hbox {VSR}}–hbox {QED}_{3} explicitly.

Influence of the pseudoscalar condensate gradient on the cooling regime of compact stars

We consider the processes in compact stars that arise during the potential formation of a pseudoscalar condensate in finite volumes. We do not propose specific hypotheses about the nature of this condensate. Considering that in the regions with a changing pseudoscalar density, photon propagation can be described in the framework of Maxwell–Chern–Simons electrodynamics, we find the reflection/transmission coefficients for regions with different densities. We study the fermion spectrum in the presence of an axial field considering the pseudoscalar condensate gradient. We also study the influence of the modified photon and fermion spectra on the cooling process of compact stars.

SIM(1)–VSR Maxwell–Chern–Simons electrodynamics

In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges are derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.

The functional squeeze operator algebra in Maxwell–Chern–Simons electrodynamics

Using annihilation and creation squeeze operators, we construct a basis of Hermitian generators obeying the SU(2) Lie algebra. We discuss the relations between the Maxwell–Chern–Simons electrodynamics vacuum and the normal vacuum and show that the most general Bogoliubov transformation is just a functional rotation in the Fock space.

Markovian versus non-Markovian stochastic quantization of a complex-action model

We analyze the Markovian and non-Markovian stochastic quantization methods for a complex action quantum mechanical model analog to Maxwell–Chern–Simons electrodynamics in Weyl gauge. We show through analytical methods convergence to the correct equilibrium state for both methods. Introduction of a memory kernel generates a non-Markovian process which has the effect of slowing down oscillations that arise in the Langevin-time evolution towards equilibrium of complex-action problems. This feature of non-Markovian stochastic quantization might be beneficial in large-scale numerical simulations of complex action field theories on a lattice.

Emergent gauge dynamics of highly frustrated magnets

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern–Simons electrodynamics expected of a Z2 spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step toward a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and toward a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.

Symmetries of field equations of axion electrodynamics

The group classification of models of axion electrodynamics with arbitrary self-interaction of axionic field is carried out. It is shown that extensions of the basic Poincar\'e invariance of these models appear only for constant and exponential interactions. The related conservation laws are discussed. The maximal continuous symmetries of the 3d Chern-Simons electrodynamics and Carroll-Field-Jackiw electrodynamics are presented. Using the In\"on\"u-Wigner contraction the nonrelativistic limit of equations of axion electrodynamics is found. Exact solutions for the electromagnetic and axion fields are discussed including those which describe propagation with group velocities faster than the speed of light. However these solutions are causal since the corresponding energy velocities are subluminal.

NONCOMMUTATIVITY IN MAXWELL–CHERN–SIMONS-MATTER THEORY SIMULATES PAULI MAGNETIC COUPLING

We study interactions between like charges in the noncommutative Maxwell–Chern–Simons electrodynamics minimally coupled to spinors or scalars. We demonstrate that the nonrelativistic potential profiles, for only spatial noncommutativity, are nearly identical to the ones generated by a non-minimal Pauli magnetic coupling, originally introduced by Stern.12 Although the Pauli term has crucial roles in the context of physically relevant objects such as anyons and like-charge bound states (or "Cooper pairs"), its inception12 (see also Ref. 13) was ad hoc and phenomenological in nature. On the other hand, we recover similar results by extending the minimal model to the noncommutative plane, which has developed into an important generalization to ordinary spacetime in recent years. No additional input is needed besides the noncommutativity parameter. We prove a novel result that for complex scalar matter sector, the bound states (or "Cooper pairs") can be generated only if the Maxwell–Chern–Simons-scalar theory is embedded in noncommutative spacetime. This is all the more interesting since the Chern–Simons term does not directly contribute a noncommutative correction term in the action.

Remarks on charged vortices in the Maxwell–Chern–Simons model

We study vortex-like configuration in Maxwell–Chern–Simons electrodynamics. Attention is paid to the similarity it shares with the Nielsen–Olesen solutions at large distances. A magnetic symmetry between a point-like and an azimuthal-like current in this framework is also pointed out. Furthermore, we address the issue of a neutral spinless particle interacting with a charged vortex, and obtain that the Aharonov–Casher-type phase depends upon mass and distance parameters.

A planar Runge–Lenz vector

Following Dahl’s method an exact Runge–Lenz vector M with two components M1 and M2 is obtained as a constant of motion for a two particle system with charges e1 and e2 whose electromagnetic interaction is based on Chern–Simons electrodynamics. The Poisson bracket {M1,M2}≠Lz but is modified by the appearance of the product e1e2 as central charges.

Equilibrium in quantum systems of particles with magnetic interaction. Fermi and bose statistics

Quantum systems of particles interacting via an effective electromagnetic potential with zero electrostatic component are considered (magnetic interaction). It is assumed that the j th component of the effective potential for n particles equals the partial derivative with respect to the coordinate of the jth particle of “magnetic potential energy” of n particles almost everywhere. The reduced density matrices for small values of the activity are computed in the thermodynamic limit for d-dimensional systems with short-range pair magnetic potentials and for one-dimensional systems with long-range pair magnetic interaction, which is an analog of the interaction of three-dimensional Chern-Simons electrodynamics (“magnetic potential energy” coincides with the one-dimensional Coulomb (electrostatic) potential energy).

Spinors in Non-relativistic Chern–Simons Electrodynamics

It is shown that the non-relativistic “Dirac” equation of Lévy-Leblond, we used recently to describe a spin 12 field interacting non-relativistically with a Chern–Simons gauge field, can be obtained by lightlike reduction from 3+1 dimensions. This allows us to prove that the system is Schrödinger symmetric. A spinor representation of the Schrödinger group is presented. Static, self-dual solutions, describing spinor vortices are given and shown to be the non-relativistic limits of the fermionic vortices found by Choet al. The construction is extended to external harmonic and uniform magnetic fields.

On the Coleman-Hill theorem

The Coleman-Hill theorem prohibits the appearance of radiative corrections to the topological mass (more precisely, to the parity-odd part of the vacuum polarization tensor at zero mementum) in a wide class of abelian gauge theories in 2+ 1 dimensions. We re-express the theorem in terms of the effective action rather than in terms of the vacuum polarization tensor. The theorem so restated becomes somewhat stronger: a known exception to the theorem, spontaneously broken scalar Chern-Simons electro-dynamics, obeys the new non-renormalization theorem. Whereas the vacuum polarization does receive a one-loop, parity-odd correction, this does not translate to a radiative contribution to the Chern-Simons term in the effective action. We also point out a new situation, involving scalar fields and parity-odd couplings, which was overlooked in the orginal analysis, where the conditions of the theorem are satisfied and where the topological mass does, in fact, get a radiative correction.

Charge screening in the Higgs phase of Chern-Simons electrodynamics.

Though screened at large distances, a point-like electric charge can still participate in a long-range electromagnetic interaction in the Higgs phase, namely that with the Aharonov-Bohm field produced by a localized magnetic flux. We show that this follows from the fact that the screening charge, induced in the presence of a Higgs condensate, does not interact with the Aharonov-Bohm field. The same phenomenon occurs, if a Chern-Simons term is incorporated in the action. This observation provides a physical basis for the recently proposed classification of the superselection sectors of this model in terms of a quasi-Hopf algebra.

Fermionic vortex solutions in Chern-Simons electrodynamics.

We present anyonic vortex solutions made of real electrons which could be interpreted as nontopological solitons of the (2+1)-dimensional Chern-Simons electrodynamics. The {ital n}-soliton solutions, which we obtain by imposing an effective axial symmetry on the (3+1)-dimensional quantum electrodynamics, have 4{ital n} real parameters which represent the position, size, and phase of each soliton.

Photon as a goldstone boson in (2 + 1)-dimensional abelian gauge theories

We examine the relationship between the masslessness of a photon and the realization of global symmetries in abelian gauge theories in 2 + 1 dimensions: scalar and spinor QED and their immediate generalizations. We find that this masslessness (in the Coulomb phase) directly follows from the spontaneous breakdown of a symmetry generated by the magnetic flux. In spinor QED with two flavours the chiral symmetry is broken as well but a linear combination of the flux and chiral symmetries remains unbroken. A similar symmetry breaking pattern U(1) ⊗ U(1) → U(1) is realized also in Chern-Simons electrodynamics for a particular value of the Chern-Simons coefficient at which the photon becomes massless (anyon superconductor). The pertinent order parameter for the Higgs-Coulomb phase transition in scalar QED is identified with the vev of the magnetic vortex creation operator V( x). We calculate, using weak coupling perturbation theory, the vev and the correlator of V( x) in both phases. This turns out to be equivalent to evaluation of the euclidean QED partition function in the presence of the external current which produces a magnetic monopole (with the contribution of the Dirac string subtracted). In the Higgs phase this vev vanishes in accord with the Wigner-Weyl realization of the flux symmetry. In the Coulomb phase of scalar QED we obtain a nonzero value of the order parameter whereas in the spinor QED it vanishes. This indicates that in the scalar QED the symmetry breaking is of the usual Nambu-Goldstone type while in the spinor QED it is of Kosterlitz-Thouless type.

MASSLESSNESS OF PHOTON AND CHERN-SIMONS TERM IN (2 + 1)-DIMENSIONAL QED

We study the realization of global symmetries in (2 + 1)-dimensional QED with two fermion flavors. It is shown that, in a certain range of mass parameters, the chiral symmetry [Formula: see text] and the flux symmetry Φ = ∫d2xB are both spontaneously broken, but the combination I = Q5 − sign (m)e/πΦ remains unbroken. The photon is identified with the corresponding massless excitation, which is required in this case by Goldstone theorem. An order parameter vanishes and chiral and flux symmetries are realized in the Kosterlitz-Thouless mode. Outside this range of parameters the vacuum is symmetric and simultaneously the photon's topological mass is generated. Similar symmetry breaking pattern U (1) ⊗ U (1) → U (1) is realized in Chern-Simons electrodynamics for a particular value of the bare CS-term coefficient at which the "statistical photon" becomes massless. We point out the direct correspondence of this model to the superconducting anyon gas.