Geodesic
A~$(2+1)$-Dimensional Gauge Model with Electrically Charged Fermions
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 3, pp. 396-409

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We consider a $(2+1)$-dimensional gauge theory with a nonzero fermion density and an initial Chern–Simons topological term, whose Lorentz invariance is spontaneously broken in a certain Lorentz reference frame by the generation of a constant homogenous magnetic field. We propose interpreting the number $\eta=\pm1$, which characterizes the two nonequivalent representations of Dirac matrices in $2+1$ dimensions, as a quantum number that explicitly describes the spin of the fermion. In particular, this interpretation allows determining the vacuum state of the model in a constant homogenous magnetic field as the state whose fermion and spin numbers are equal to zero.
Mots-clés : fermion charge
Keywords: spin, Chern–Simons topological term, spontaneous symmetry breaking, effective Lagrangian. 
@article{TMF_2004_140_3_a3,
     author = {V. R. Khalilov},
     title = {A~$(2+1)${-Dimensional} {Gauge} {Model} with {Electrically} {Charged} {Fermions}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {396--409},
     publisher = {mathdoc},
     volume = {140},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_140_3_a3/}
}
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V. R. Khalilov. A~$(2+1)$-Dimensional Gauge Model with Electrically Charged Fermions. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 3, pp. 396-409. http://geodesic.mathdoc.fr/item/TMF_2004_140_3_a3/