Hsu, J. P. ; Sudarshan, E. C. G. (1974) Theory of massive and massless YangMills fields Physical Review D  Particles, Fields, Gravitation and Cosmology, 9 (6). pp. 16781686. ISSN 15507998

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Official URL: http://prd.aps.org/abstract/PRD/v9/i6/p1678_1
Related URL: http://dx.doi.org/10.1103/PhysRevD.9.1678
Abstract
Introducing the Lagrangian multiplier field χ^{→}(x), a canonical formalism for the YangMills fields f^{→}_{μ}(x) with mass M≥0 is proposed within the framework of an indefinitemetric quantum field theory. The formalism for the massive f^{→}_{μ} has a welldefined zeromass limit, and the reduction of the physical components of f^{→}_{μ} 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+(□+M^{2})^{−1}gf^{→}_{μ}×∂^{μ})]^{−½}≡D_{M}^{−½} for the massive f^{→}_{μ}, and that the extra factor is D_{M≡0}^{−1} for the massless f^{→}_{μ} 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.
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