Abstract
New coherent states of theq-Weyl algebraAA † −qA † A = 1,0 <q < 1, are constructed. They are defined as eigenstates of the operatorA † which is the lowering operator for nonhighest weight representations describing positive energy states. Depending on whether the positive spectrum is discrete or continuous, these coherent states are related either to the bilateral basic hypergeometric series or to some integrals over them. The free particle realization of theq-Weyl algebra whenA † A ∞ d2/dx2 is used for illustrations.
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On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia.