Light propagation in 
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-dimensional electrodynamics: The case of linear constitutive laws

Goulart, E.; Bittencourt, Eduardo; Brandão, Elliton O. S.

doi:10.1103/physreva.106.063521

Cited by 2 publications

(6 citation statements)

References 27 publications

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“…There are two possible approaches to dimensional reduction. The first and most common one consists in formulating a lower dimensional version of the theory in 3 + 1 dimensions, characterized by the same ab initio properties of the starting point, as long as they are allowed by the new dimensionality [26][27][28][29][30][31][32]. An alternative approach is represented by the method of descent.…”

Section: Introductionmentioning

confidence: 99%

Dimensional reduction of the Dirac theory

Angelone

Ercolessi²,

Facchi³

et al. 2023

J. Phys. A: Math. Theor.

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We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field, by applying Hadamard's method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical electromagnetic field, governed by the Dirac-Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an electromagnetic field provides a more complicated theory in 2+1 dimensions, in which the method of descent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered.

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Section: Introductionmentioning

confidence: 99%

Dimensional reduction of the Dirac theory

Angelone

Ercolessi²,

Facchi³

et al. 2023

J. Phys. A: Math. Theor.

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show abstract

“…Contrarily to the linear case in vacuum [19,20,27], it is possible to see again [17] the role of the constitutive relations in the non-equivalence between a two-form formulation of electrodynamics in (3 + 1)-dimensions and the (2 + 1)-dimensional one developed here. In particular, our constitutive relations (7) and ( 8) involve objects with different tensor ranks and, obviously, the number of degrees of freedom is distinct in each case.…”

Section: Discussionmentioning

confidence: 84%

“…Here, we shall follow the steps of our previous work [17], dealing with the electromagnetic field being represented by a two-form field F ab . The main difference with respect to our previous analysis is the assumption of a timelike observer field that will decompose F ab , from the very beginning, in terms of a vector electric field and a (pseudo) scalar magnetic field.…”

Section: Mathematical Settingmentioning

confidence: 99%

“…It is worth mentioning that equation (29) gives rise to a homogeneous quadratic multivariate polynomial at the cotangent bundle. In the case of linear constitutive laws, the precise form of this polynomial was rigorously derived in [17], using the method of the effective metric. In principle, such an observer-independent and totally covariant approach could be carried out for the nonlinear case as well.…”

Section: Phase Velocitiesmentioning

confidence: 99%

“…Based mostly upon the results derived in [17], where the effective metric associated with a genuine (2 + 1)-dimensional electrodynamics with a linear constitutive law was derived, we now turn our attention to quite general nonlinear constitutive laws. More specifically, we determine the general expressions for the phase velocities and the corresponding wavepolarization vectors for nonlinear dielectrics, nonlinear magnetoelectric media, and a combination thereof.…”

Section: Introductionmentioning

confidence: 99%

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Light propagation in ( 2+1 )-dimensional electrodynamics: the case of nonlinear constitutive laws

Bittencourt

Brandão

Goulart

2023

J. Phys. A: Math. Theor.

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We scrutinize the geometrical properties of light propagation inside a hypotheticalnonlinear medium modeled by a fully covariant electromagnetic theory in (2+1)-dimensions.After setting the local and nonlinear constitutive relations, the phase velocity and thepolarization of the waves are derived and three special cases are analyzed in detail. Inparticular, we show that this version of electromagnetism in low dimensions may presentphenomena such as one-way propagation and controlled opacity, among others, for a largeclass of dielectric and magneto-electric parameters.

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Light propagation in (2+1) -dimensional electrodynamics: The case of linear constitutive laws

Cited by 2 publications

References 27 publications

Dimensional reduction of the Dirac theory

Dimensional reduction of the Dirac theory

Light propagation in ( 2+1 )-dimensional electrodynamics: the case of nonlinear constitutive laws

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