Galilean conformal algebras in two spatial dimension

Details Galilean conformal algebras in two spatial dimension Galilean conformal algebras in two spatial dimension

2011-12-03

arxiv.org/abs/1112.0634v1

Physics

Mathematical Physics

20 pages

Scientific paper

An infinite dimensional Galilean conformal algebra g in (2+1) dimensional space-time is studied. We give a classification of all possible central extensions of g. Then representation theory of the algebra with the central extensions, denoted by tilde{g} is developed. It is shown that tilde{g} with unit central charge is realized in terms of infinitely many kinds of bosons. We then derive explicit formula of Kac determinant for the Verma modules of tilde{g}. It is seen from the formula that the Verma modules are irreducible for nonvanishing highest weights. Finally, we introduce new infinite dimensional Galilean conformal algebra in the space-time of same dimension. Its central extensions are also discussed.

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