TY - JOUR

T1 - Spin, angular momentum and spin-statistics for a relativistic quantum many-body system

AU - Horwitz, Lawrence

PY - 2013/1/25

Y1 - 2013/1/25

N2 - The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wave packets and admitting covariant expectation values for the coordinate operator xμ introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch-Gordan coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many-body systems and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are briefly discussed.

AB - The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wave packets and admitting covariant expectation values for the coordinate operator xμ introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch-Gordan coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many-body systems and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are briefly discussed.

UR - http://www.scopus.com/inward/record.url?scp=84871569449&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/3/035305

DO - 10.1088/1751-8113/46/3/035305

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AN - SCOPUS:84871569449

SN - 1751-8113

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 3

M1 - 035305

ER -