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@article{29842, author = {Chowdhury, S. Hasibul Hassan and Ali, S. Twareque and Engliš, Miroslav}, article_location = {Bristol (England)}, article_number = {19}, doi = {http://dx.doi.org/10.1088/1751-8121/aa66a6}, keywords = {coherent states; Berezin-Toeplitz quantization; reproducing kernel; noncommutative geometry}, language = {eng}, issn = {1751-8113}, journal = {Journal of Physics A: Mathematical and Theoretical}, title = {Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization}, url = {http://iopscience.iop.org/article/10.1088/1751-8121/aa66a6/meta}, volume = {50}, year = {2017} }
TY - JOUR ID - 29842 AU - Chowdhury, S. Hasibul Hassan - Ali, S. Twareque - Engliš, Miroslav PY - 2017 TI - Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization JF - Journal of Physics A: Mathematical and Theoretical VL - 50 IS - 19 SP - „195203-1“-„195203-19“ EP - „195203-1“-„195203-19“ PB - IOP Publishing Ltd SN - 17518113 KW - coherent states KW - Berezin-Toeplitz quantization KW - reproducing kernel KW - noncommutative geometry UR - http://iopscience.iop.org/article/10.1088/1751-8121/aa66a6/meta L2 - http://iopscience.iop.org/article/10.1088/1751-8121/aa66a6/meta N2 - In this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of G(nc), a connected, simply connected nilpotent Lie group, which was identified as the kinematical symmetry group of noncommutative quantum mechanics for a system of two degrees of freedom in an earlier paper. Similarly described are the degenerate noncommutative coherent states arising from the degenerate UIRs of Gnc. We then compute the reproducing kernels associated with both these families of coherent states and study the Berezin-Toeplitz quantization of the observables on the underlying 4-dimensional phase space, analyzing in particular the semi-classical asymptotics for both these cases. ER -
CHOWDHURY, S. Hasibul Hassan, S. Twareque ALI a Miroslav ENGLIŠ. Noncommutative coherent states and related aspects of Berezin-Toeplitz quantization. \textit{Journal of Physics A: Mathematical and Theoretical}. Bristol (England): IOP Publishing Ltd, roč.~50, č.~19, s.~„195203-1“-„195203-19“, 19 s. ISSN~1751-8113. doi:10.1088/1751-8121/aa66a6. 2017.
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