Details
| Original language | English |
|---|---|
| Article number | 149 |
| Number of pages | 23 |
| Journal | International Journal of Theoretical Physics |
| Volume | 63 |
| Issue number | 6 |
| Publication status | Published - 14 Jun 2024 |
Abstract
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.
Keywords
- Bundle, Frobenius, Helicity, Interacting representation, Massless, Smoothness of generators
ASJC Scopus subject areas
- Mathematics(all)
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: International Journal of Theoretical Physics, Vol. 63, No. 6, 149, 14.06.2024.
Research output: Contribution to journal › Article › Research › peer review
}
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 -