ar X iv : q ua nt - p h / 04 09 11 8 v 1 17 S ep 2 00 4 THE SEGAL – BARGMANN TRANSFORM FOR NONCOMPACT SYMMETRIC SPACES OF THE COMPLEX TYPE
نویسنده
چکیده
We consider the generalized Segal–Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal–Bargmann transform is a unitary map onto a certain L space of meromorphic functions. For general functions, we give an inversion formula for the Segal–Bargmann transform, involving integration against an “unwrapped” version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.
منابع مشابه
ar X iv : q ua nt - p h / 04 11 17 2 v 1 2 3 N ov 2 00 4 Information and Entropy in Quantum Theory
متن کامل
ar X iv : q ua nt - p h / 04 09 15 5 v 1 23 S ep 2 00 4 Orientations of two coupled molecules
Orientation states of two coupled polar molecules controlled by laser pulses are studied theoretically. By varying the period of a series of periodically applied laser pulse, transition from regular to chaotic behavior may occur. Schmidt decomposition is used to measure the degree of entanglement. It is found that the entanglement can be enhanced by increasing the strength of laser pulse. PACS:...
متن کاملar X iv : q ua nt - p h / 03 09 02 9 v 1 2 S ep 2 00 3 Rule ( 4 ) and Continuous Observation Richard
The effect of rule (4) on a series or parallel sequence of quantum mechanical steps is to insure that a conscious observer does not skip a step. This rule effectively places the observer in continuous contact with the system.
متن کاملThe Segal–bargmann Transform for Noncompact Symmetric Spaces of the Complex Type
We consider the generalized Segal–Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal–Bargmann transform is a unitary map onto a certain L space of meromorphic functions. For general functions, we give an inversion formula for the Segal–Bargmann transform, involving integration against an “...
متن کاملar X iv : q ua nt - p h / 97 09 04 2 v 1 18 S ep 1 99 7 Measurement and state preparation via ion trap quantum computing
We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'Helon and G. The performance of a measurement shows some interesting patterns which are closely related to searching.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004