TY - JOUR

T1 - Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

AU - Adorno, T. C.

AU - Baldiotti, M. C.

AU - Gitman, D. M.

PY - 2010/12/15

Y1 - 2010/12/15

N2 - We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a θ modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the θ-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (à la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the θ-modified Pauli equation. We extract θ-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a θ modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal Einstein-Podolsky-Rosen states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity. This allows us to estimate an upper bound on the noncommutativity parameter.

AB - We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a θ modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the θ-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (à la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the θ-modified Pauli equation. We extract θ-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a θ modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal Einstein-Podolsky-Rosen states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity. This allows us to estimate an upper bound on the noncommutativity parameter.

UR - http://www.scopus.com/inward/record.url?scp=78651302251&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.82.123516

DO - 10.1103/PhysRevD.82.123516

M3 - Article

AN - SCOPUS:78651302251

SN - 1550-7998

VL - 82

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 12

M1 - 123516

ER -