Gauge covariance relations and the fermion propagator in Maxwell–Chern–Simons QED3

Bashir, Adnan; Raya, Alfredo; Madrigal, S Sánchez

doi:10.1088/1751-8113/41/50/505401

Cited by 16 publications

(26 citation statements)

References 60 publications

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“…Interestingly, for the RQED case, the parameter θ in front of the CS term is not a mass, as for QED 3 , but somehow acts as a dimensionless suppressing factor in the photon propagator (see (14)). Moreover, we computed the exact value of θ in case the four-component Dirac fermions are massive for two different realizations of the mass term, both relevant for graphene studies, see (38) and (39) which is valid for both Lorentz invariant and non-invariant case.…”

Section: Discussionmentioning

confidence: 99%

“…We can see that the mass terms (38) and (39) have different relative sign for the two flavours + and −.…”

Section: B Four-component Vs Two-component Spinorsmentioning

confidence: 95%

“…The Coleman-Hill theorem [25] guarantees that no higher order corrections are allowed, so the connection of the two terms is clearly pictured. On the other hand, the presence of a CS term generates dynamically a Haldane mass for the fermions [39] already at one-loop as well.…”

Section: Setting the Stage: Planar Systems And Rqedmentioning

confidence: 99%

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Remarks on the Chern-Simons photon term in the QED description of graphene

2018

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We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this non-local but still gauge invariant theory, we can confirm that the topological piece of the photon self-energy at zero momentum does not receive further quantum corrections apart from the potential one-loop contribution, even when considering the Lorentz non-invariant case due to the Fermi velocity v F < c. This is of relevance to probe possible time parity odd dynamics in a planar sheet of graphene which has an effective description in terms of (2 + 1)-dimensional planar reduced QED.Keywords: Reduced QED, dynamical Chern-Simons term. * david.dudal@kuleuven.be † ana.mizher@kuleuven.be ‡ pablo.pais@kuleuven.be I. CONTEXT AND MOTIVATIONQuantum Electrodynamics in (2 + 1) dimensions (QED 3 ) has been widely used as a toy model for Quantum Chromodynamics (QCD). This is due to the fact that although being Abelian, QED 3 exhibits similar features as non-Abelian gauge theories, making it possible, for instance, to map and investigate chiral symmetry breaking and confinement into it [1][2][3][4][5]. The similarity is reinforced by the fact that a non-Abelian gauge theory at high temperature suffers a dimensional reduction and, if coupled to N f fermion families, the non-Abelian interactions are suppressed by a factor of N −1 f , so that in the large N f limit the theory can be considered approximately Abelian.Recently, the emergence of the so-called Dirac and Weyl planar materials [6], converted QED 3 into a playground in which a potential link between high energy physics (including quantum fields in curved spacetimes) and condensed matter can emerge [7][8][9][10][11][12][13]. Those are materials in which, due to the specific structure of their underlying lattice, the charge carriers present a relativistic-like behavior, being correctly described by a Dirac-like equation in some regimes. Particularly, the physical realization of graphene and other materials in two space dimensions, that are proved to contain a priori massless Dirac spinors, naturally yields the fermionic part of QED 3 [14, 15] through the continuum limit of the tight-binding theory, usually applied to describe their conduction electrons, which in turn implies a direct connection to QCD, as discussed above.Nevertheless, even though in these systems the fermions are constrained to remain in-plane and therefore are correctly described by a theory in (2 + 1) dimensions, the gauge fields responsible for the interaction between these electrons are not subject to the same constraint. One of the most remarkable consequences of this fact is that the interaction between electrons remains the familiar ∼ 1/r potential rather than the logarithmic one that would take place if the gauge fields were also restricted to the plane. Therefore, it is convenient and necessary to modify QED 3 in order to merge the desired features of the two sectors of the theory, starting with a general (3 + 1) theory and dimensionally reducing it to a non-local effective (2 ...

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Section: Discussionmentioning

confidence: 99%

“…We can see that the mass terms (38) and (39) have different relative sign for the two flavours + and −.…”

Section: B Four-component Vs Two-component Spinorsmentioning

confidence: 95%

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Remarks on the Chern-Simons photon term in the QED description of graphene

2018

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“…This term breaks the time reversal symmetry, and gives a mass to the photon. It is important in condensed matter physics in the context of chiral symmetry breaking [6][7][8][9], high temperature superconductivity [10] and the Hall effect [11]. CS terms can dynamically generate magnetic fields in QED 2+1 [12], and magnetic fields are thought to influence dynamical symmetry breaking in a universal and model independent way through what is known as magnetic catalysis (for a review see [13]).…”

Section: Introductionmentioning

confidence: 99%

Effect of a Chern-Simons term on dynamical gap generation in graphene

Carrington

2019

Phys. Rev. B

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We study the effect of a Chern-Simons term on dynamical gap generation in a low energy effective theory that describes some features of mono-layer suspended graphene. We use a nonperturbative Schwinger-Dyson approach. We solve a set of coupled integral equations for eight independent dressing functions that describe fermion and photon degrees of freedom. We find a strong suppression of the gap, and corresponding increase in the critical coupling, as a function of increasing Chern-Simons coefficient.

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“…Particularly often, the multi-flavor theory with the limit N → ∞ has been used, since it avoids infrared problems, which usually become troublesome in lower number of dimensions. The other important point in this analysis has been the unpleasant gauge dependence of the nonperturbative results which constitute the common problem of the approximated studies based on DS equations [6,9,10,16,21,22].…”

Section: Introductionmentioning

confidence: 99%

Infrared Self-consistent Solutions of Bispinor QED3

Radożycki

2013

Acta Phys. Pol. B

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Quantum electrodynamics in three dimensions in the bispinor formulation is considered. It is shown that the Dyson-Schwinger equations for fermion and boson propagators may be self-consistently solved in the infrared domain if on uses Salam's vertex function. The parameters defining the behavior of the propagators are found numerically for different values of coupling constant and gauge parameter. For weak coupling, the approximated analytical solutions are obtained. The renormalized gauge boson propagator (transverse part) is shown in the infrared domain to be practically gauge independent.

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Gauge covariance relations and the fermion propagator in Maxwell–Chern–Simons QED₃

Cited by 16 publications

References 60 publications

Remarks on the Chern-Simons photon term in the QED description of graphene

Remarks on the Chern-Simons photon term in the QED description of graphene

Effect of a Chern-Simons term on dynamical gap generation in graphene

Infrared Self-consistent Solutions of Bispinor QED<sub><span class="cmr-7">3</span></sub>

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