Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-02
Phys.Lett.B699:129-134,2011
Physics
High Energy Physics
High Energy Physics - Theory
v3: 1+12 pages, with typos corrected in PLB proofs included
Scientific paper
10.1016/j.physletb.2011.03.059
Using the notion of Galilean conformal algebra (GCA) in arbitrary space dimension d, we introduce for d=3 quantized nonrelativistic counterpart of twistors as the spinorial representation of O(2,1){\oplus}SO(3) which is the maximal semisimple subalgebra of three-dimensional GCA. The GC-covariant quantization of such nonrelativistic spinors, which shall be called also Galilean twistors, is presented. We consider for d=3 the general spinorial matrix realizations of GCA, which are further promoted to quantum-mechanical operator representations, expressed as bilinears in quantized Galilean twistors components. For arbitrary Hermitian quantum-mechanical Galilean twistor realizations we obtain the result that the representations of GCA with positive-definite Hamiltonian do not exist. For non-positive H we construct for N{\geq}2 the Hermitian Galilean N-twistor realizations of GCA; for N=2 such realization is provided explicitly.
Fedoruk Sergey
Kosinski Piotr
Lukierski Jerzy
Maslanka Pawel
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