Witten deformed exterior derivative and Bessel functions
Abstract
In a recent paper we investigated the internal space of Bessel functions associated with their orders. We found a formula (new) unifying Bessel functions of integer and of real orders. In this paper we study the deformed exterior derivative system $H=d_{\lambda}$ on the puctured plane as a tentative to understand the origin of the formula and find that indeed similar formula occurs. This is no coincidence as we will demonstrate that generating functions of integer order Bessel functions and of real orders are respectively eigenstates of the usual exterior derivative and its deformation. As a direct consequence we rediscover the unifying formula and learn that the system linear in $d_{\lambda}$ is related to Bessel theory much as the system quadratic in ($d_{\lambda}+d_{\lambda}^{*}$) is related to Morse theory.
 Publication:

arXiv eprints
 Pub Date:
 July 2000
 DOI:
 10.48550/arXiv.mathph/0007017
 arXiv:
 arXiv:mathph/0007017
 Bibcode:
 2000math.ph...7017M
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  Functional Analysis;
 Mathematics  Mathematical Physics
 EPrint:
 8 pages latex