LIE Groups- a Physical Approach
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Date
1995
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Addis Ababa University
Abstract
symmetries playa vital role in physics. If interactions
are not knolm precisely, the underlying symmetries reflected in
the phenomenology, provide valuable i.nformation on the interactions,
even when interactions are knOlm symmetries continue to remain a
great asset.
We concentrate on continuous symmetries. Associated with
these are their Lie groups and algebras. \'Ie take up the study of
such algebras following the very elegant approach due to Schl'linger
starting from the bilinear products of fermion or boson creation
operators a wide variety of Lie algebras can be generated. That,
such algebras are relevant to physics follows from the simple fact
that such bilinear products figure frequently in physical problems.
Our aim is:
a) to study the general classification of such algebras,
b) to study their broad general characterstics,
c) to apply them to physical problems.
The applications vie choose to study are principally from
elementary particle and nuclear physics and many body theories.
The accidental degeneracies encountered in quantum mechanics are
easily understood in this algebraic framework. Our principal
objective is to grasp the essentials I'lithout recourse to Ul1\'larranted
mathematics and to learn to use these techniques in physical
problems
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Physical Approach