@article{52de88f15ebe445dbb490c5b3c81db85,

title = "Reformulation of general relativity as a gauge theory",

abstract = "The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called {"}spin frame,{"} are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials Bμ are introduced and corresponding fields Fμν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of Bμ are generalized spin coefficients, and linear combinations of Fμν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.",

author = "M. Carmeli and S. Malin",

note = "Funding Information: Interest in gauge fields started out when Weyl observed that electromagnetism can be formulated as a gauge theory, and continued with Yang and Mills{\textquoteright} gauge theory of strong interactions [I]. In recent years, since Salam and Weinberg introduced spontaneously broken gauge theories which unify weak and electromagnetic interactions [2, 31 and especially since {\textquoteleft}t Hooft proved that these theories are renormalizable [4], gauge theories became a prime subject of research in theoretical physics. The present work is a formulation of a gauge theory of gravitation in spinor affine space-time which reduces, in the special case of metric (Riemannian) space-time, to general relativity in the Newman-Penrose formalism [5]. Spinor affine space-timesa re defined in Section 3B, and are the analog of affinely connected manifolds when spinor * This work was supported by the Israel National Academy of Sciences. t Work supported in part by the Colgate Research Council. This work was done while SM. was visiting the Ben Gurion University.",

year = "1977",

month = jan,

day = "1",

doi = "10.1016/0003-4916(77)90270-6",

language = "English",

volume = "103",

pages = "208--232",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

number = "1",

}