Theq-boson operator algebra andq-Hermite polynomials

✍ Scribed by J. Jeugt

• Book ID: 104768687
• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 304 KB
• Volume: 24
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00420486

✦ Synopsis

The q-boson algebra is defined as an associative algebra with generators and relahons. Some examples are given, and then the q-boson algebra is extended such that the roots of the 'diagonal generators' are also defined. It is shown that a family of transformahons exist mapping one set of standard generators of the q-boson algebra to another set of standard generators. Using such a transformation, one obtains expressions for q-bosons for which the kth q-boson state is expressed in terms of a q-Hermite polynomial pt(x; q) which reduces to the ordinary Hermite polynomial of degree k when q -1. (1991). 33C45, 81T05.

Mathematics Subject Classifications