Theory of massive and massless Yang-Mills fields

Hsu, J. P. ; Sudarshan, E. C. G. (1974) Theory of massive and massless Yang-Mills fields Physical Review D - Particles, Fields, Gravitation and Cosmology, 9 (6). pp. 1678-1686. ISSN 1550-7998

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Introducing the Lagrangian multiplier field χ(x), a canonical formalism for the Yang-Mills fields fμ(x) with mass M≥0 is proposed within the framework of an indefinite-metric quantum field theory. The formalism for the massive fμ has a well-defined zero-mass limit, and the reduction of the physical components of fμ as M→0 is embodied in an elegant way. Using the field equation for χ (x) and the path integral, we find that the "extra" factor in the amplitude due to the interaction of χ (x) in the intermediate states is [det(1+(□+M2)−1gfμ×∂μ)]−½≡DM−½ for the massive fμ, and that the extra factor is DM≡0−1 for the massless fμ because of their different degrees of observable freedom. Thus, the resultant rules for the Feynman diagrams for M > 0 and M=0 are not smoothly connected. The theory is covariant, renormalizable, and unitary after the extra parts are removed from the amplitudes. The problems of unitarization and renormalizability are discussed.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:51041
Deposited On:27 Jul 2011 13:07
Last Modified:18 May 2016 05:07

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