Lie Groups- A Physical Approach

symmetries playa vital role in physics. If interactionsrnare not knolm precisely, the underlying symmetries reflected inrnthe phenomenology, provide valuable i.nformation on the interactions,rneven when interactions are knOlm symmetries continue to remain arngreat asset.rnWe concentrate on continuous symmetries. Associated withrnthese are their Lie groups and algebras. 'Ie take up the study ofrnsuch algebras following the very elegant approach due to Schl'lingerrnstarting from the bilinear products of fermion or boson creationrnoperators a wide variety of Lie algebras can be generated. That,rnsuch algebras are relevant to physics follows from the simple factrnthat such bilinear products figure frequently in physical problems.rnOur aim is:rna) to study the general classification of such algebras,rnb) to study their broad general characterstics,rnc) to apply them to physical problems.rnThe applications vie choose to study are principally fromrnelementary particle and nuclear physics and many body theories.rnThe accidental degeneracies encountered in quantum mechanics arerneasily understood in this algebraic framework. Our principalrnobjective is to grasp the essentials I'lithout recourse to Ul1'larrantedrnmathematics and to learn to use these techniques in physicalrnproblems

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