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 TMF, 1977, Volume 32, Number 1, Pages 34–43 (Mi tmf3106)

Covariant formulation of relativistic Hamiltonian theory on the light cone

N. M. Atakishiyev, R. M. Mir-Kassimov, Sh. M. Nagiyev

Abstract: In the covariant formulation of relativistic hamiltonian theory given in [1–3] the momenta of all physical particles belong to the mass shell. In the vertices of diagrams the total 4-momentum of physical particles and the additional spurion line is conserved. The momentum of the spurion is proportional to the constant time-like vector on which the on-shell $S$-matrix does not depend. In the present paper a version of relativistic hamiltonian theory is developed in which the 4-momentum of the spurion lies on the light cone. Essentially new point in this scheme is a specific regularisation, by means of which the singularities present in all theories formulated in the light cone variables are removed in all diagrams. The unitarity and causality conditions are analysed in detail. It is shown that the choice of the regularisation is determined by the causality condition.

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English version:
Theoretical and Mathematical Physics, 1977, 32:1, 579–585

Citation: N. M. Atakishiyev, R. M. Mir-Kassimov, Sh. M. Nagiyev, “Covariant formulation of relativistic Hamiltonian theory on the light cone”, TMF, 32:1 (1977), 34–43; Theoret. and Math. Phys., 32:1 (1977), 579–585

Citation in format AMSBIB
\Bibitem{AtaMirNag77} \by N.~M.~Atakishiyev, R.~M.~Mir-Kassimov, Sh.~M.~Nagiyev \paper Covariant formulation of relativistic Hamiltonian theory on the light cone \jour TMF \yr 1977 \vol 32 \issue 1 \pages 34--43 \mathnet{http://mi.mathnet.ru/tmf3106} \transl \jour Theoret. and Math. Phys. \yr 1977 \vol 32 \issue 1 \pages 579--585 \crossref{https://doi.org/10.1007/BF01041430} 

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This publication is cited in the following articles:
1. N. B. Skachkov, I. L. Solovtsov, “Covariant three-dimensional formulation of the composite quark model of mesons”, Theoret. and Math. Phys., 41:2 (1979), 977–986
2. N. B. Skachkov, I. L. Solovtsov, “Description of the form factor of a relativistic two-particle system in the covariant Hamiltonian formulation of quantum field theory”, Theoret. and Math. Phys., 43:3 (1980), 494–502
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