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New Approach to the U(2,2)‐Symmetry in Spinor and Gravitation Theory
Author(s) -
Slawianowski Jan J.
Publication year - 1996
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190440203
Subject(s) - tetrad , physics , mathematical physics , general relativity , gravitation , spinor , gauge theory , gravitational field , classical field theory , classical unified field theories , theoretical physics , einstein field equations , classical mechanics
Generally‐relativistic Dirac equation is reinterpreted as an approximation to the more fundamental model based on the quadruplet of Klein‐Gordon particles with the internal hermitian metric of the neutral signature (++−−). Compensating field of the local group U(2,2) of internal symmetries splits under the GL(2, C)‐reduction into gravitational co‐tetrad, Einstein‐Cartan‐Weyl affine connection, and an auxiliary co‐tetrad‐like object. Equation for the matter field shows under the SL(2,C)‐reduction a reasonable correspondence with the generally relativistic Dirac theory. Masses of fermions may be dynamically generated by non vanishing “vacuum” values of geometrodynamical quantities. There is also a convincing correspondence between Yang‐Mills equations for the U(2,2)‐gauge field and the Einstein‐Cartan theory, or more general metric‐affine theories of gravitation. In our approach the tetrad field is neither a reference frame nor a compensating field of translations in originally Minkowskian space, but a part of the U(2,2)‐gauge multiplet.