TY - JOUR

T1 - Bundle Structure of Massless Unitary Representations of the Poincaré Group

AU - Dragon, Norbert

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/6/14

Y1 - 2024/6/14

N2 - Reviewing the construction of induced representations of the Poincaré group of four-dimensional spacetime we find all massive representations, including the ones on interacting many-particle states. Massless momentum wavefunctions of non-vanishing helicity turn out to be more precisely sections of a U(1)-bundle over the massless shell, a property which to date was overlooked in quantum field theory and in bracket notation. Our traditional notation of states in Hilbert space enables questions about square integrability and smoothness. Their answers complete the picture of relativistic quantum physics. Frobenius reciprocity prohibits massless one-particle states with total angular momentum less than the modulus of the helicity. There is no two-photon state with J=1, explaining the longevity of orthopositronium. Partial derivatives of the momentum wave functions are no operators in the space of massless states with nonvanishing helicity. They allow only for covariant, noncommuting derivatives. The massless shell has a noncommutative geometry with helicity being its topological charge.

AB - Reviewing the construction of induced representations of the Poincaré group of four-dimensional spacetime we find all massive representations, including the ones on interacting many-particle states. Massless momentum wavefunctions of non-vanishing helicity turn out to be more precisely sections of a U(1)-bundle over the massless shell, a property which to date was overlooked in quantum field theory and in bracket notation. Our traditional notation of states in Hilbert space enables questions about square integrability and smoothness. Their answers complete the picture of relativistic quantum physics. Frobenius reciprocity prohibits massless one-particle states with total angular momentum less than the modulus of the helicity. There is no two-photon state with J=1, explaining the longevity of orthopositronium. Partial derivatives of the momentum wave functions are no operators in the space of massless states with nonvanishing helicity. They allow only for covariant, noncommuting derivatives. The massless shell has a noncommutative geometry with helicity being its topological charge.

KW - Bundle

KW - Frobenius

KW - Helicity

KW - Interacting representation

KW - Massless

KW - Smoothness of generators

UR - http://www.scopus.com/inward/record.url?scp=85195899050&partnerID=8YFLogxK

U2 - 10.1007/s10773-024-05612-z

DO - 10.1007/s10773-024-05612-z

M3 - Article

AN - SCOPUS:85195899050

VL - 63

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

SN - 0020-7748

IS - 6

M1 - 149

ER -