Abstract
After a brief review of the field formulations and the relativistic non-instantaneous action-at-a-distance formulations of some well known classical theories, we study Rivacoba’s generalization of a theory with a linearly rising potential as a relativistic non-instantaneous action-at-a-distance theory. For this case we construct the corresponding field theory, which turns out to coincide with a model proposed by Kiskis to describe strong interactions. We construct the action functional for this field theory. Although this model belongs to the class of Lagrangian theories with higher derivatives, it is shown that its action-at-a-distance counterpart has a much simpler form. A proposal to construct an action-at-a-distance description of Yang-Mills interactions is also presented.
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References
Wheeler, J.A., Feynman, R.P.: Rev. Mod. Phys. 17, 157 (1945)
Wheeler, J.A., Feynman, R.P.: Rev. Mod. Phys. 21, 425 (1949)
Dettman, J.W., Schild, A.: Phys. Rev. 95, 1057 (1954)
Dyer, J., Schild, A.: J. Math. Anal. Appl. 4, 328 (1962)
Hoyle, F., Narlikar, J.V.: Proc. R. Soc., Ser. A 282, 191 (1964)
Andersen, C.M., von Baeyer, H.C.: Ann. Phys. 60, 67 (1970)
Schild, A.: Ann. Phys. 93, 88 (1975)
Ramond, P.: Phys. Rev. D 7, 449 (1973)
Katz, A.: J. Math. Phys. 10, 1929 (1969)
Katz, A.: J. Math. Phys. 10, 2215 (1969)
Degasperis, A.: Phys. Rev. D 3, 273 (1971)
Cornwall, J.M.: Nucl. Phys. B 128, 75 (1977)
Rivacoba, A.: Nuovo Cimento B 84, 35 (1984)
Weiss, J.: J. Math. Phys. 27, 1015 (1986)
Kalb, M., Ramond, P.: Phys. Rev. D 9, 2273 (1974)
Jensen, B., Lindstrom, U.: Phys. Lett. B 398, 83 (1997)
Friedman, J., Uryu, K.: Phys. Rev. D 73, 104039 (2006)
Bel, L., Fustero, X.: Ann. Inst. Henri Poincaré, a Phys. Théor. 25, 411 (1976)
Droz-Vincent, P.: Lett. Nouvo Cimento 1, 839 (1969)
Todorov, I.T.: In: Llosa, J. (ed.) Relativistic Action at a Distance: Classical and Quantum Aspects. Lectures Notes in Physics, vol. 162. Springer, Berlin (1982)
Horwitz, L.P., Rohrlich, F.: Phys. Rev. D 24, 1528 (1981)
Sazdjian, H.: Ann. Phys. 136, 136 (1981)
Longhi, G., Dominici, D., Gomis, J., Lobo, J.A.: In: Llosa, J. (ed.) Relativistic Action at a Distance: Classical and Quantum Aspects. Lectures Notes in Physics, vol. 162. Springer, Berlin (1982)
Droz-Vincent, P.: Hamiltonian two-body system in special relativity (2010). arXiv:1006.5443 [math-ph]
Ben-Ya’acov, U.: J. Phys. A, Math. Theor. 42, 225401 (2009)
De Luca, J.: Phys. Rev. E 82, 026212 (2010)
Kiskis, J.: Phys. Rev. D 11, 2178 (1975)
Barut, A.O.: Electrodynamics and Classical Theory of Fields and Particles. Dover, New York (1980)
Moore, R.A., Scott, T.C., Monagan, M.B.: Phys. Rev. Lett. 59, 525 (1987)
Hoyle, F., Narlikar, J.V.: Lectures on Cosmology and Action at a Distance Electrodynamics. World Scientific, Singapore (1996)
Schild, A.: Phys. Rev. 131, 2762 (1963)
Louis-Martinez, D.J.: Phys. Lett. A 320, 103 (2003)
Anderson, J.L.: Principles of Relativity Physics. Academic Press, New York (1967)
Louis-Martinez, D.J.: Phys. Lett. B 632, 733 (2006)
Louis-Martinez, D.J.: Phys. Lett. A 364, 93 (2007)
Allen, T.J., Olsson, M.G.: Phys. Rev. D 68, 054022 (2003)
Jugeau, F., Sazdjian, H.: Nucl. Phys. B 670, 221 (2003)
Allen, T., Olsson, M., Yuan, Y., Schmidt, J., Veseli, S.: Phys. Rev. D 70, 054012 (2004)
Rubakov, V.: Classical Theory of Gauge Fields. Princeton University Press, Princeton (2002)
Kosyakov, B.: Introduction to the Classical Theory of Particles and Fields. Springer, Berlin (2007)
Wong, S.K.: Nuovo Cimento A 65, 689 (1970)
Kosyakov, B.: J. Phys. A, Math. Theor. 41, 465401 (2008)
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Louis-Martinez, D.J. Relativistic Action at a Distance and Fields. Found Phys 42, 215–223 (2012). https://doi.org/10.1007/s10701-011-9589-5
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DOI: https://doi.org/10.1007/s10701-011-9589-5