منابع مشابه
On Generalized Uncertainty Principle
We study generalized uncertainty principle through the basic concepts of limit and Fourier transformation to analyze the quantum theory of gravity or string theory from the perspective of a complex function. Motivated from the noncommutative nature of string theory, we have proposed a UV/IR mixing dependent function δ̃(∆x,∆k, ǫ). We arrived at the string uncertainty principle from the analyticit...
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A theorem of Hardy states that, if f is a function on R such that |f(x)| ≤ C e−α|x|2 for all x in R and |f̂(ξ)| ≤ C e−β|ξ|2 for all ξ in R, where α > 0, β > 0, and αβ > 1/4, then f = 0. Sitaram and Sundari generalised this theorem to semisimple groups with one conjugacy class of Cartan subgroups and to the K-invariant case for general semisimple groups. We extend the theorem to all semisimple gr...
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Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principl...
متن کاملSome Remarks on the Discrete Uncertainty Principle
We give a survey of recent results related to the uncertainty principle for finite groups. We begin by discussing the abelian case, and give a simplified proof of a theorem of Tao in the case of cyclic groups. We then discuss variations of this theme and make some remarks in the non-abelian case.
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Realizing the canonical commutation relations (CCR) [N, 0] = — i as N = — i d/d9 and 0 to be the multiplication by 9 on the Hilbert space of square integrable functions on [0, 27t], in the physical literature there seems to be some contradictions concerning the Heisenberg uncertainty principle (AN) (A0) > 1/4. The difficulties may be overcome by a rigorous mathematical analysis of the domain of...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2016
ISSN: 0024-6093,1469-2120
DOI: 10.1112/blms/bdw006