Nonrelativistic counterparts of twistors and the realizations of Galilean conformal algebra

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 SO(2,1)⊕SO(3) which is the maximal semisimple subalgebra of three-dimensional GCA. The GC-covariant quantizat...

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Bibliographic Details
Published in:Physics letters. B 2011-05, Vol.699 (1-2), p.129-134
Main Authors: Fedoruk, S., Kosiński, P., Lukierski, J., Maślanka, P.
Format: Article
Language:English
Subjects:
Algebra
Conformal algebra
Construction
Elementary particles
Nonrelativistic symmetries
Operators
Quantization
Representations
Twistors
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Summary: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 SO(2,1)⊕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⩾2 the Hermitian Galilean N-twistor realizations of GCA; for N=2 such realization is provided explicitly.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2011.03.059