Summary
We discuss a unified model of gauge theories for gravitational and electroweak interactions. Herefore we embed both gauge groups in one group and then construct different symmetry-breaking steps to arrive at massive fermion level.
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References
F. Ghaboussi andH. Dehnen:Phys. Rev. D,33, 2205 (1986);Int. J. Theor. Phys.,26, 486 (1987);27, 576 (1988). Furthermore seeF. Ghaboussi, H. Dehnen andM. Israelit:Phys. Rev. D,35, 1189 (1987).
Although we obtained in [1] only a linearized version of Einstein equations, however it is possible to perform a modified version of «full» Einstein equations in a suitable gauge condition usually applied by Einstein himself (to be published).
We mean hereby the (Glashow-Salam-Weinberg)SU(2)L×U(1) model, see hereforeC. Itzykson andI. B. Zuber:Quantum Field Theory (McGraw-Hill, New York, N.Y., 1980).
In this paper we are mainly interested in the model construction, thus we discuss only briefly a «qualitative» relation of the light-deflection type.
We consider here two-spinor representations of fermions, thus the foundamental representation ofSU(4) contains a doublet of left-handed (L) isospinors.
We take, roughly speaking, the coupling constant ofSU(4) as {g}, which is {g}={g G,g W,g′} depending on the coupling of gauge bosons in lower energy levels. Theg′ belongs to the rest interaction related to the quotient gauge group (SU(4)/SU(2)G×SU(2)L). Thus theU(1) has its own constantg 1. In the high-energy levels (∼1019 GeV) there is only two coupling constantsg andg 1. In the lower energies different coupling constantsg′,g G andg W are drifting from each other in the same manner as in grand unified models (SU(5),SO(10),…); since all coupling constants here are, as functions of energy, running coupling constants.
See hereforeF. Ghaboussi:Int. J. Theor. Phys.,26, 957 (1987) and references quoted therein.
To see this explicitly recall that one may transform fields in question orthogonally («Weinberg rotation») within the unitary gauge models. The reason is simply that the eigenstates of mass matrix (operator) are not the same as the eigenstates of electroweak interaction operators.
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Ghaboussi, F. A unified gravito-electroweak gauge field model. Nuov Cim A 104, 1475–1481 (1991). https://doi.org/10.1007/BF02817430
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DOI: https://doi.org/10.1007/BF02817430