Volume 3 Number 4 December 1999

TAIWANESE JOURNAL OF MATHEMATICS

Vol. 3, No. 4, pp. 529-538, December 1999

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AN INFINITE-DIMENSIONAL HEISENBERG UNCERTAINTY PRINCIPLE

　

Yuh-Jia Lee^* and Aurel Stan^**

　
Abstract.

An analogue of the classical Heisenberg inequality is given for an infinite-dimensional space. The proof relies on a commutation relationship and integration by parts formula for Gaussian measure. We also discuss when the equality holds.

　

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Received February 10, 1998; revised January 4, 1999.

Communicated by H.-H. Kuo.

1991 Mathematics Subject Classification: 46E50, 81T99, 60H99, 28C20, 60B05.

Key words and phrases: Gaussian measure, second quantization, Heisenberg uncertainty principle.

* Research supported by the National Science Council of Taiwan.

** Research supported by U.S. Army Research Office grant #DAAH04-94-G-0249.

	AN INFINITE-DIMENSIONAL HEISENBERG UNCERTAINTY PRINCIPLE
	Yuh-Jia Lee^* and Aurel Stan^**
	Abstract.
	An analogue of the classical Heisenberg inequality is given for an infinite-dimensional space. The proof relies on a commutation relationship and integration by parts formula for Gaussian measure. We also discuss when the equality holds.