Summary
The canonical formalism for a neutral scalar field on a lightlike hyperplane is studied in terms of Dirac's theory for constrained Hamiltonian systems. The field and its canonical momentum on the plane are restricted to appropriate functional spaces and are expanded into wave packets. The formalism becomes simpler by the absence of unphysical modes forP −=0. After quantization we discuss how the Wightman function loses its dynamical information when it is restricted to the lightlike plane.
Riassunto
Si studia il formalismo canonico per un campo neutro scalare in un iperpiano del tipo della luce in termini della teoria di Dirac per sistemi hamiltoniani con vincoli. Il campo e il suo impulso canonico sul piano sono ristretti a spazi funzionali appropriati e sono sviluppati in pacchetti d'onde. Il formalismo diventa più semplice per l'assenza di modi non fisici perP −=0. Dopo la quantizzazione si discute come la funzione di Wightman perda la sua informazione dinamica quando è ristretta al piano del tipo della luce.
Резюме
Исследуется канонический формализм для нейтрального скалярного поля на светоподобной гиперплоскости в терминах теории Дирака для ограниченных гамильтонианных систем. Поле и его канонический импульс на плоскости ограничены соответствующими функциональными пространствами и разлагаются на волновые пакеты. Предложенный формализм становится проще из-за отсутствия нефизических мод дляP −=0. После квантования мы обсуждаем, как функция Вайтмана утрачивает динамическую информацию, когда она ограничена на светоподобной плоскости.
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References
P. A. M. Dirac:Rev. Mod. Phys.,21, 392 (1949). There exist too many references to be cited here. We quote only two articles below, which contain earlier references:H. Leutwyler, J. R. Klauder andL. Streit:Nuovo Cimento,66 A, 536 (1970);J. B. Kogut andD. E. Soper:Phys. Rev. D,1, 2901 (1970).
P. A. M. Dirac:Can. Journ. Math.,2, 129 (1950);Proc. Roy. Soc.,246 A, 326 (1958).
L. Banyai andL. Mezincescu:Rev. Roum. Phys.,18, 1035 (1973);A. J. Hanson, T. Regge andC. Teitelboim:Constrained Hamiltonian systems, Academia Nazionale dei Lincei, Rome, to be published;H. Yabuki: preprint (RIMS-183);P. Senjanovic: preprint (CCNY-HEP-75/6).
M. Ida:Lett. Nuovo Cimento,15, 249 (1976);T. Maskawa andK. Yamawaki:Prog. Theor. Phys.,56, 270 (1976);M. Huszár:J. Phys. A,9, 1359 (1976).
N. Nakanishi andH. Yabuki: preprint (RIMS-204);N. Nakanishi andK. Yamawaki: preprint (RIFP-277).
T. Suzuki, S. Tameike andE. Yamada:Prog. Theor. Phys.,55, 922 (1976);C. R. Hagen andJ. H. Yee: preprint (UR-607).
S. Schlieder andE. Seiler:Comm. Math. Phys.,25, 62 (1972).
L. Streit: to appear in theProceedings of the XIII Winter School for Theoretical Physics, Karpacz, 1976.
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Address after April 1977: Research Institute for Fundamental Physics, Kyoto University, Kyoto, Japan.
Traduzione a cura della Redazione.
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Ida, M. Canonical formalism on a lightlike hyperplane. Nuov Cim A 40, 354–367 (1977). https://doi.org/10.1007/BF02776868
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DOI: https://doi.org/10.1007/BF02776868