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 TMF, 2005, Volume 143, Number 2, Pages 258–277 (Mi tmf1814)

Construction of form factors of composite systems by a generalized Wigner–Eckart theorem for the Poincaré group

A. F. Krutova, V. E. Troitskyb

a Samara State University
b Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: We generalize the previously developed relativistic approach for electroweak properties of two-particle composite systems to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. We use a special mathematical technique to parameterize matrix elements of electroweak current operators in terms of form factors. The parameterization is a realization of the generalized Wigner–Eckart theorem for the Poincaré group, used when considering composite-system form factors as distributions corresponding to reduced matrix elements. The electroweak-current matrix element satisfies the relativistic covariance conditions and also automatically satisfies the conservation law in the case of an electromagnetic current.

Keywords: Wigner–Eckart theorem, Poincaré group, form factors, composite systems, relativistic Hamiltonian dynamics

DOI: https://doi.org/10.4213/tmf1814

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English version:
Theoretical and Mathematical Physics, 2005, 143:2, 704–719

Bibliographic databases:

Citation: A. F. Krutov, V. E. Troitsky, “Construction of form factors of composite systems by a generalized Wigner–Eckart theorem for the Poincaré group”, TMF, 143:2 (2005), 258–277; Theoret. and Math. Phys., 143:2 (2005), 704–719

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf1814
• https://doi.org/10.4213/tmf1814
• http://mi.mathnet.ru/eng/tmf/v143/i2/p258

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Krutov AF, Troitsky VE, “Deuteron tensor polarization component T-20(Q(2)) as a crucial test for deuteron wave functions”, Physical Review C, 75:1 (2007), 014001
2. Krutov, AF, “Asymptotic behavior of the deuteron form factors in the two-nucleon model and electron scattering experiments at GeV energies at JLab”, Physical Review C, 78:4 (2008), 044002
3. Krutov, AF, “Asymptotic estimation of some multiple integrals and the electromagnetic deuteron form factors at high momentum transfer”, Journal of Physics A-Mathematical and Theoretical, 41:25 (2008), 255401
4. Krutov A.F., Lisienkova M.V., Troitsky V.E., “Semileptonic decays of mesons in Poincaré-invariant potential model”, International Workshop on Quantum Optics 2007, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 7024, 2008, 2409–2409
5. Krutov A.F., Troitsky V.E., Tsirova N.A., “Mathematical analysis of the asymptotic behavior of the electromagnetic deuteron form factors at high momentum transfer”, International Workshop on Quantum Optics 2007, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), 7024, 2008, 2410–2410
6. Krutov, AF, “Instant form of Poincaré,-invariant quantum mechanics and description of the structure of composite systems”, Physics of Particles and Nuclei, 40:2 (2009), 136
7. V. V. Andreev, A. F. Krutov, “Elektromagnitnye formfaktory mezonov”, PFMT, 2011, no. 1(6), 7–19
8. Troitsky S.V., Troitsky V.E., “Transition From a Relativistic Constituent-Quark Model to the Quantum-Chromodynamical Asymptotics: a Quantitative Description of the Pion Electromagnetic Form Factor at Intermediate Values of the Momentum Transfer”, Phys. Rev. D, 88:9 (2013), 093005
9. A. F. Krutov, R. G. Polezhaev, V. E. Troitsky, “Describing radiation decay using the instant form of relativistic quantum mechanics”, Theoret. and Math. Phys., 184:2 (2015), 1148–1162
10. Krutov A.F. Polezhaev R.G. Troitsky V.E., “Radius of the Rho Meson Determined From Its Decay Constant”, Phys. Rev. D, 93:3 (2016), 036007
11. V. V. Andreev, V. Yu. Gavrish, A. F. Krutov, “Metodika vychisleniya elektroslabykh kharakteristik mezonov v puankare-invariantnoi kvantovoi mekhanike”, PFMT, 2018, no. 1(34), 7–19
12. Troitsky S.V., Troitsky V.E., “Linking Infrared and Ultraviolet Parameters of Pion-Like States in Strongly Coupled Gauge Theories”, Eur. Phys. J. C, 78:11 (2018), 899
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