Physical origin of topological mass in 2 + 1 dimensions

Vacuum polarization for neutral particles in 2 + 1 dimensions

“…Vacuum induced spin (S) and angular momentum (J) were also studied for charged particles in the literature [5][6][7]13]. Translated to our case, we have for finite Q the following results.…”

“…Vacuum polarization for charged Dirac particles in 2+1 dimensions has been studied by many authors in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The subject is relevant to many other physical problems in field theory, such as parity violation, Chern-Simons theory [15][16], flavor symmetry breaking, etc.…”

Chiral tunnelling and the Klein paradox in graphene

“…The term chirality is often used to refer to the additional built-in symmetry between electron and hole parts of graphene's spectrum (as indicated by color in Fig. 1) and is analogous (although not completely identical 11,16 ) to the chirality in three-dimensional QED.…”

Self-consistent solutions for vacuum currents around a magnetic flux string

“…[8,9]. It is found that setting m = O at the outset leads to a vanishing induced charge density p( r ) and thus zero total charge, while the topological invariant Q = -( eF/2 )sgn( rn ), independent of 1 m 1, is not altered if we take the limit m-0.…”

“…The total induced charge Q is found to be a topological invariant proportional to the spectral asymmetry of the Dirac operator Q = -e P / 2 , with F the total magnetic flux, 0 5 F 5 1 [1, 5,6]. For a spatially uniform BGF, the feedback interactions of the vacuum currents are manifested by an effective photon mass e2/4.rr [2,7,8].…”