Related papers: Uncertainty principles associated with the linear …
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…
The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon \ell ^{2}$, $\ell $ being a length and $\epsilon$ a $\pm$ sign. The…
We establish anisotropic uncertainty principles (UPs) for general metaplectic operators acting on $L^2(\mathbb{R}^d)$, including degenerate cases associated with symplectic matrices whose $B$-block has nontrivial kernel. In this setting,…
We derive the uncertainty principle for a Dirac fermion in a torsion field obeying the Hehl-Datta (HD) equation. We first discuss that there should be a correction factor to the Heisenberg uncertainty principle (HUP) when torsional effects…
In this article, we establish the $L^p$-Heisenberg-Pauli-Weyl uncertainty inequalities on the Laguerre hypergroup $\mathbb{K}$, the natural setting for radial analysis on the Heisenberg group. For $1 \leq p < 2$, under the condition $b >…
The aim of this article is to formulate some novel uncertainty principles for the continuous shearlet transforms in arbitrary space dimensions. Firstly, we derive an analogue of the Pitt's inequality for the continuous shearlet transforms,…
In the present work we are concerned with the development of a new uncertainty principle based on wavelet transform in the Clifford analysis/algebras framework. We precisely derive a sharp Heisenberg-type uncertainty principle for the…
A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also…
Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty…
The purpose of this article is to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform (QFT). We study some fundamental properties of this extension such as scaling, translation,…
We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we establish a real Paley-Wiener theorem for the linear…
We consider a non-canonical phase-space deformation of the Heisenberg-Weyl algebra that was recently introduced in the context of quantum cosmology. We prove the existence of minimal uncertainties for all pairs of non-commuting variables.…
A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.
We discuss the Generalized Uncertainty Principle and the Extended Uncertainty Principle in the context of black hole solutions coming from non-local theories of gravity, focusing, specifically, on Infinite Derivative Gravity. We argue that…
In this paper, we study forms of the uncertainty principle suggested by problems in control theory. We obtain a version of the classical Paneah-Logvinenko-Sereda theorem for the annulus. More precisely, we show that a function with spectrum…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for…
In this paper, we obtained the Dunkl analogy of classical Lp Hardy inequality for $p > N + 2\gamma$ with sharp constant $\left(\frac{p-N-2\gamma}{p}\right)^{p}$, where $2\gamma$ is the degree of weight function associated with Dunkl…
We will establish the Caffarelli-Kohn-Nirenberg type inequalities with non-doubling weights being permitted. The classical Caffarelli-Kohn-Nirenberg type inequalities are categorized into non-critical and critical cases, and it is known…