Relativistic crystalline symmetry breaking and anyonic states in magnetoelectric superconductors

Abstract

There exists a connection between the creation of toroidal moments (TM) and the breaking of the one-cell relativistic crystalline symmetry (RCS) associated to any given crystal [1] into which non-trivial magnetoelectric coupling effects (ME) exist [2] . Indeed, in this kind of crystals, any interaction between a charge carrier and an elementary magnetic cell can breaks the RCS of this previous given cell by varying, in the simplest case, the continuous defining parameters of the initial RCS.This breaking can be associated to a change of the initial Galilean proper frame of any given carrier to an "effective" one, into which the RCS of the interacting cell is kept. We can speak of a kind of "inverse" kineto-magnetoelectric effect [3]. The magnetic groups compatible with such process have been computed [1]. Moreover, one can notice that the TM's break the P and T symmetries but not the PT one as in anyons theories [4,5]. This breaking creates so-called Nambu-Goldstone bosons generating "effective" magnetic monopoles. These consequences allow us to claim, first, that anyons are

Navigation of Space-Time Ships in Unified Gravitational and Electromagnetic Waves.

“…the spin of an electron). This generalized precession could give a possible origin for the creation of anyons in high-T c superconductors [48] and might be an alternative to Chern-Simon theory. Also, the tensor (χ k,h ) might be a polarization tensor of some matter and the particle would be "dressed" with this kind of polarization.…”

“…with (x 0 , â â â1 0 ≡ a a a 1 0 ) ∈ P 1 ⊂ J 1 (R n ), and P 1 being the set of elements satisfying relations (40a) with c 0 = 0. Similarily the Pfaff system we denote P 1 over P 1 and generated by the 1-forms Ω j K in (42) with |K| ≤ 1, is locally integrable on every neighborhood U(x 0 , a a a 1 0 ) ⊂ P 1 , since at the point (x 0 , a a a 1 0 ) we have relations (47) with |J| ≤ 1 together with relations (48).…”

“…with Ω i jk satisfying (48) for any given Ω h L with |L| ≤ 1, and where the tensors χ are defined on P 2 . Together, they define a back connection, and the tensors χ define a connection if they satisfy the relations:…”