Summary
The Yang-Mills dynamical variables in the presence of gravitation are presented in terms of new variables by means of a null-tetrad and spin coefficient method. The Yang-Mills equations in curved space are consequently written in the null-tetrad method. The resulting equations then resemble the Newman-Penrose version of Maxwell’s equations extended to a non-Abelian gauge group. A special consideration is then given to the flat-space case, thus recovering the usual Yang-Mills theory, but now written in the null-tetrad method. The advantages of the new approach to the Yang-Mills equations are illustrated by considering the problem of exact solutions of these equations both in the presence and in the absence of gravitation.
Riassunto
Si presentano le variabili dinamiche di Yang-Mills in presenza di gravità, sulla base di nuove variabili per mezzo del metodo di una tetrade nulla e dei coefficienti di spin. Le equazioni di Yang-Mills nello spazio curvo sono soritte di conseguenza secondo il metodo della tetrade nulla. Le equazioni ricavate somigliano alla versione di Newman-Penrose delle equazioni di Maxwell estese a un gruppo di gauge non abeliano. Si dedica poi speciale attenziono al caso dello spazio piatto, reinstaurando così la solita teoria di Yang-Mills, ora enunciata però secondo il metodo della tetrade nulla. Si illustrano i vantaggi del nuovo approccio all’equazioni di Yang-Mills considerando il problema delle esatte soluzioni di queste equazioni in presenza ed in assenza di gravità.
Similar content being viewed by others
References
C. N. Yang and R. L. Mills:Phys. Rev:,96, 191 (1954).
S. Weinberg:Phys. Rev. Lett.,19, 1264 (1967).
A Salam: inElementary Particle Theory, edited by N. Svartholm (Stockholm, 1968).
G. ’tHooft:Nucl. Phys.,33 B, 173 (1971).
R. Utiyama:Phys. Rev.,101, 1597 (1956).
E. Lubkin:Ann. of Phys.,23, 233 (1963).
A. Trautman:Rep. Math. Phys.,1, 29 (1970).
C. N. Yang:Phys. Rev. D,12, 3845 (1975).
See, for example,Proceedings of the Instanton Symposium, held in Copenhagen,November 26–31, 1976.
H. Loos:Journ. Math. Phys.,8, 1870, 2114 (1967).
R. Treat:Nuovo Cimento,50, 871 (1967).
T. Eguchi:Phys. Rev. D,13, 1561 (1976).
T. T. Wu andC. N. Yang: inProperties of Matter under Unusual Conditions, edited by H. Mark and S. Fernbach (New York, N. Y., 1969), p. 349.
G. ’tHooft:Nucl. Phys.,79 B, 276 (1974).
M. Prasad andCh. Sommerfeld:Solutions of classical gauge theories with spin and internal structure, preprint; see also S. Coleman, S. Parke, N. Neven and Ch. Sommerfeld:Can one dent a dyon, preprint.
J. P. Hsu:Phys. Rev. Lett.,36, 646 (1976).
Y. M. Cho and P. G. O. Freund:Phys. Rev. D,12, 1588 (1975).
M. Y. Wang:Journ. Math. Phys.,17, 704 (1976).
F. A. Bais and R. J. Russell:Phys. Rev. D,11, 2692 (1975).
P. Yasskin:Phys. Rev. D,12, 2212 (1975).
E. T. Newman and R. Penrose:Journ. Math. Phys.,3, 566 (1962).
M. Carmeli and S. I. Fickler:Phys. Rev. D,5, 290 (1972).
M. Carmeli:Phys. Rev. D,14, 1727 (1976).
M. Carmeli:Group Theory and General Relativity (New York, N. Y., 1977).
M. Carmeli and M. Kaye:Nuovo Cimento,34 B, 225 (1976).
M. Carmeli and S. Malin:Ann. of Phys.,103, 208 (1977).
A. I. Janis and E. T. Newman:Journ. Math. Phys.,6, 902 (1965).
K. Wódkiewicz:Acta Phys. Polonica,6 B, 509 (1975).
K. Wódkiewicz:Phys. Rev. D,11, 3395 (1975).
S. Malin:Phys. Rev. D,10, 2338 (1974).
M. Carmeli:Phys. Lett.,68 B, 463 (1977).
M. Carmeli:Phys. Rev. Lett.,39, 523 (1977).
Author information
Authors and Affiliations
Additional information
To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.
Rights and permissions
About this article
Cite this article
Carmeli, M., Charac, C. & Kaye, M. Null-tetrad formulation of the Yang-Mills field equations. Nuovo Cim 45, 310–334 (1978). https://doi.org/10.1007/BF02894687
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02894687