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Register a new userGauge Covariance Relations and the Fermion Propagator in Maxwell-Chern-Simons QED3
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We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum electrodynamics (QED$_3$) considering four-component spinors with parity-even and parity-odd mass terms both for fermions and photons. Starting with its tree level expression in the Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge by means of its Landau-Khalatnikov-Fradkin transformation (LKFT). We compare our findings in the weak coupling regime with the direct one-loop calculation of the two-point Green function and observe perfect agreement up to a gauge independent term. We also reproduce results derived in earlier works as special cases of our findings.
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In a recent preprint [cond-mat/0204040] Khveshchenko questioned the validity of our computation of the gauge invariant fermion propagator in QED3, which we employed as an effective theory of high-T_c cuprate superconductors [cond-mat/0203333]. We take this opportunity to further clarify our procedure and to show that criticism voiced in the above preprint is unwarranted.
We examine the energetics of $Q$-balls in Maxwell-Chern-Simons theory in two space dimensions. Whereas gauged $Q$-balls are unallowed in this dimension in the absence of a Chern-Simons term due to a divergent electromagnetic energy, the addition of a Chern-Simons term introduces a gauge field mass and renders finite the otherwise-divergent electromagnetic energy of the $Q$-ball. Similar to the case of gauged $Q$-balls, Maxwell-Chern-Simons $Q$-balls have a maximal charge. The properties of these solitons are studied as a function of the parameters of the model considered, using a numerical technique known as relaxation. The results are compared to expectations based on qualitative arguments.
We study dynamical symmetry breaking in three-dimensional QED with a Chern-Simons (CS) term, considering the screening effect of $N$ flavor fermions. We find a new phase of the vacuum, in which both the fermion mass and a magnetic field are dynamically generated, when the coefficient of the CS term $kappa$ equals $N e^2/4 pi$. The resultant vacuum becomes the finite-density state half-filled by fermions. For $kappa=N e^2/2 pi$, we find the fermion remains massless and only the magnetic field is induced. For $kappa=0$, spontaneous magnetization does not occur and should be regarded as an external field.
We study the Cherenkov effect in the context of the Maxwell-Chern-Simons (MCS) limit of the Standard Model Extension. We present a method to determine the exact radiation rate for a point charge.
By using the Hamilton-Jacobi [$HJ$] framework the higher-order Maxwell-Chern-Simons theory is analyzed. The complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential are reported, from which all symmetries of the theory are identified. In addition, we complete our study by performing the higher order Gitman-Lyakhovich-Tyutin [$GLT$] framework and compare the results of both formalisms.
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