A measure-free approach to coherent states

作者：Horzela Andrzej^*; Szafraniec Franciszek Hugon

来源：Journal of Physics A-Mathematical and Theoretical, 2012, 45(24): 244018.

DOI：10.1088/1751-8113/45/24/244018

In the process of generalizing coherent states, the situation when the measure-which is customarily incorporated in their definition-is indeterminate becomes unavoidable. A more dramatic situation may occur if there is no measure which makes the reproducing kernel Hilbert space, involved in the construction of coherent states, isometrically included in an L-2 space. Therefore, it appears that there is a need to redefine coherent states making the definition measure-free. Starting out with the reproducing kernel property, we ensure the basic feature of coherent states-resolution of the identity-to be maintained, cf (15) and remark 2. The only investment in the whole undertaking is a sequence (Phi(n))(n=0)(d) satisfying (4); the rest, including the aforesaid resolution of the identity, is a consequence of our choice. The approach is supported by examples which make the circumstances clear under which the sequence (Phi(n))(n=0)(d) appears; moment problems or rather orthogonal polynomials are one of them.

• 出版日期2012-6-22