TY - JOUR

T1 - Induced representations of tensors and spinors of any rank in the Stueckelberg-Horwitz-Piron theory

AU - Horwitz, Lawrence P.

AU - Zeilig-Hess, Meir

N1 - Publisher Copyright:
© 2015 AIP Publishing LLC.

PY - 2015/9

Y1 - 2015/9

N2 - We show that a modification of Wigner's induced representation for the description of a relativistic particle with spin can be used to construct spinors and tensors of arbitrary rank, with invariant decomposition over angular momentum. In particular, scalar and vector fields, as well as the representations of their transformations, are constructed. The method that is developed here admits the construction of wave packets and states of a many body relativistic system with definite total angular momentum. Furthermore, a Pauli-Lubanski operator is constructed on the orbit of the induced representation which provides a Casimir operator for the Poincaré group and which contains the physical intrinsic angular momentum of the particle covariantly.

AB - We show that a modification of Wigner's induced representation for the description of a relativistic particle with spin can be used to construct spinors and tensors of arbitrary rank, with invariant decomposition over angular momentum. In particular, scalar and vector fields, as well as the representations of their transformations, are constructed. The method that is developed here admits the construction of wave packets and states of a many body relativistic system with definite total angular momentum. Furthermore, a Pauli-Lubanski operator is constructed on the orbit of the induced representation which provides a Casimir operator for the Poincaré group and which contains the physical intrinsic angular momentum of the particle covariantly.

UR - http://www.scopus.com/inward/record.url?scp=84941309266&partnerID=8YFLogxK

U2 - 10.1063/1.4928923

DO - 10.1063/1.4928923

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84941309266

VL - 56

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 092301

ER -