Pasupathy, J and Sudarshan, ECG (1980) Embedding Of NonSimple LieGroups, CouplingConstant Relations And NonUniqueness Of Models Of Unification. In: Pramana, 15 (4). pp. 327340.

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Abstract
A general derivation of the coupling constant relations which result on embedding a nonsimple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.
Item Type:  Journal Article 

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Additional Information:  Copyright of this article belongs to Indian Academy Sciences. 
Department/Centre:  Division of Physical & Mathematical Sciences > Centre for Theoretical Studies 
Date Deposited:  22 Feb 2010 07:29 
Last Modified:  19 Sep 2010 05:41 
URI:  http://eprints.iisc.ernet.in/id/eprint/22292 
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