Abstract
The present paper is a review of research on double expansions of relativistic amplitudes. In the beginning of the review the general theory of the expansion of functions stipulated in both the time-like and space-like domains is presented; then the general theory of the expansion of a scalar function and a function with spin is presented. After that various coordinate systems and matrices for the transition from certain basis functions to other ones are indicated. The review likewise considers certain corollaries deriving from the existence of relativistic expansions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literature Cited
N. Ya. Vilenkin and Ya. A. Smorodinskii, Zh. Éksperim. i Teor. Fiz., 46, 793 (1964).
I. M. Gel’fand, R. A. Minlos, and Z. Ya. Shapiro, Representation of the Rotation Group and the Lorentz Group [in Russian], Fizmatgiz, Moscow (1958).
M. A. Naimark, Linear Representations of the Lorentz Group [in Russian], Fizmatgiz, Moscow (1968).
I. M. Gel’fand, and M. I. Graev, Transactions of the Moscow Mathematical Society [in Russian], Vol. 11 (1962), p. 243.
I. M. Gel’fand, M. I. Graev, and N. Ya. Vilenkin, Integral Geometry and Problems of Representation Theory Associated with It [in Russian], Fizmatgiz, Moscow (1962).
I. S. Shapiro, Dokl. Akad. Nauk SSSR, 106, 647 (1956).
N. Ya. Vilenkin, Matem. Sbornik, 68 (100), No. 3, 432 (1965).
G. I. Kuznetsov, Zh. Éksperim. i Teor. Fiz., 51, 216 (1966).
G. I. Kuznetsov, Zh Éksperim. i Teor. Fiz., 54, 1756 (1968).
V. L. Ginzburg and I. E. Tamm, Zh. Éksperim. i Teor. Fiz., 17, 227 (1947).
G. I. Kuznetsov and Ya. A. Smorodinskii, Yadernaiya Fizika, 3, 383 (1966).
J. F. Boyce, J. Math and Phys., 8, 675 (1967).
A. K. Agamaliev, N. M. Atakishev, and I. A. Verdiev, Yadernaya Fizika, 10, 187 (1969).
M. Jacob and G. C. Wick, Ann. Phys., 7, 404 (1959).
Chou Huan-Chao and L. B. Zastavenko, Zh. Éksperim. i Teor, Fiz., 35, 1417 (1968).
V. S. Popov, Zh. Éksperim. i Teor. Fiz., 37, 116 (1969).
G. I. Kuznetsov, et al., Yadernaya Fizika, 10, 641 (1969).
A. R. Edmonds, Angular Momenta in Quantum Mechanics, Princeton (1957).
Nguyen Van Hieu and Dau Vong Dyk, Dokl. Akad. Nauk SSSR, 137, 1281 (1967).
I. A. Verdiev, Zh. Éksperim. i Teor. Fiz., 55, 1173 (1968);
I. A. Verdiev and L. A. Dadashev, Yadernaya Fizika, 6, 1094 (1967).
S. Ström, Arkiv Fys., 29, 467 (1965).
A. Z. Dolginov, Zh. Éksperim. i Teor. Fiz., 30, 746 (1956).
A. Z. Dolginov and I. N. Toptygin, Zh. Éksperim. i Teor. Fiz., 35, 794 (1968); 37, 1441 (1969).
A. Z. Dolginov and A. N. Moskalev, Zh. Éksperim. i Teor. Fiz., 37, 1697 (1969).
M. A. Liberman, Ya. A. Smorodinskii, and M. B. Sheftel’, Yadernaya Fizika, 7, 202 (1967).
Ya. A. Smorodinskii, Zh. Éksperim. i Teor. Fiz., 45, 604 (1963).
M. S. Marinov and V. I. Roginskii, Nucl. Phys., 49, 251 (1963).
T. Z. Trueman and G. C. Wick, Ann. Phys., 26, 322 (1964).
O. A. Atkinson, Crossing Symmetry for Helicity Amplitudes, Preprint RI 19–20 (1964).
E. L. Surkov, Yadernaya Fizika, 1, 1113 (1965).
N. A. Liberman and A. A. Makarov, Yadernaya Fizika, 9, 1314 (1959).
S. Störm, Arkiv Fys., 34, 295 (1967).
R. L. Delburgo, K. Koller, and P. Mahanta, Nuovo Cimento, 52A, 1254 (1967).
D. A. Akyeampong, J. F. Boyce, and M. A. Rushid, Nuovo Cimento, L111, 737 (1968).
J. S. Lomont and M. E. Moses, J. Math, and Phys., 3, 405 (1963).
N. Ya. Vilenkin, Special Functions and Theory of Group Representations [in Russian], Nauka, Moscow (1966).
I. Ya. Pomeranchuk, Zh. Éksperim. i Teor. Fiz., 34, 725 (1968).
N. N. Meiman, in: Problems in Elementary-Particle Physics, Vol. 4 [Russian translation], Izd. Akad. Nauk Arm. SSR, Erevan (1964), p. 258.
V. B. Barestetskii, Uspekhi Fiz. Nauk, 26, 25 (1962).
G. I. Kuznetsov and Ya. A. Smorodinskii, Yadernaya Fizika, 6, 1308 (1967).
M. Toller, Nuovo Cimento, 37, 631 (1965).
A. Sciarrini and M. J. Toller, Math. and Phys., 8, 1252 (1967).
M. Toller and I. Sertorio, Nuovo Cimento, 33, 413 (1964).
M. Toller, Nuovo Cimento, 52A, 671 (1968).
R. Delburgo, A. Salam, and J. Strathdee, J. Phys. Lett., 25B, 230 (1957).
T. Winternitz, Ya. A. Smorodinskii, and M. B. Sheftel, Yadernaya Fizika, 9, 1 (1968).
M. A. Liberman, Yadernaya Fizika, 10, 882 (1968).
I. S. Shapiro, Zh. Éksperim. i Teor. Fiz., 43, 1727 (1962).
D. V. Volkov and V. N. Gribov, Zh. Éksperim. i Teor. Fiz., 44, 1068 (1963).
M. L. Goldberger and G. E. Jones, Phys. Rev., 150, 1260 (1966);
D. Freedman and J. Wang, Phys. Rev., 153, 1596 (1967);
D. Freedman, C. E. Jones, and J. Wang, Phys. Rev., 155, 1645 (1967);
G. Domocos, Phys. Rev., 159, 1387 (1967);
D. Freedman and J. Wang, Phys. Rev. Lett., 18, 863 (1967);
G. Domocos, Phys. Lett., 24B 293 (1967);
L. Durand, Phys. Rev., 154, 1537 (1967);
J. C. Taylor, Preprint 19–16, Oxford (1967);
M. A. Liberman, Yadernaya Fizika, 9, 665 (1969).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1972 Consultants Bureau
About this chapter
Cite this chapter
Liberman, M.A., Kuznetsov, G.I., Smorodinskii, Y.A. (1972). Two-Dimensional Expansions of Relativistic Amplitudes. In: Bogolyubov, N.N. (eds) Particles and Nuclei. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-7556-2_4
Download citation
DOI: https://doi.org/10.1007/978-1-4684-7556-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-7558-6
Online ISBN: 978-1-4684-7556-2
eBook Packages: Springer Book Archive