Quantum dynamics of massive particles in a non-commutative two-sheeted space–time

Abstract

We study a formal extension of the Dirac equation in the framework of a non-commutative twosheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which can then be identified as matter and hidden-matter states. Our model exhibit several interesting features that could have observational consequences. Among them, we predict a small electromagnetic coupling between matter and hidden matter universes which should lead to matter/hidden matter oscillations in presence of intense electromagnetic vector potentials.

Experimental limits on neutron disappearance into another braneworld

“…In previous works [15][16][17][18][19], two of the present authors (Sarrazin and Petit) have shown that for a bulk containing at least two parallel 3-branes hidden to each other, matter swapping between these two worlds should occur. The particle must be massive, can be electrically charged 1 or not, but must be endowed with a magnetic moment.…”

“…From Ref. [16], we get g < 3 × 10 10 m −1 from the millicharge constraint ε < 4.1 × 10 −5 [38]. Even with more recent and stringent constraints [13,39], we get g < 9 × 10 7 m −1 from ε < 3 × 10 −10 (see Berezhiani and Lepidi in Ref.…”

“…Testing the existence of branes or extra dimensions is therefore becoming a fundamental challenge. Such evidences are expected to be obtained through high energy collisions [2][3][4], but it has been also demonstrated that some detectable effects could also be observed at low energy [2,3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] . This is the topic of the present paper.…”

“…In previous works [15,16], it was shown that in a Universe containing two parallel braneworlds invisible to each other, the quantum dynamics of a spin−1/2 fermion can be described by a two-brane Pauli equation at low energies. For a neutron outside a nucleus, in electromagnetic and gravitational fields, the relevant equations can be written as [15]:…”

Matter Localization and Resonant Deconfinement in a Two-Sheeted Space–time

“…(2) [31]. The incorporation of the electromagnetic field in the model can be done quite easily [30][31][32]. The usual U(1) gauge field must be substituted by an extended U(1) U(1) gauge relevant for the discrete Z 2 structure of the universe.…”