Related papers: Uncertainty relations on nilpotent Lie groups
The author investigates the general Lie algebra of operators of coordinates, momenta, and Lorentz group generators, which can be used in quantum gravity, theories with generalized uncertainty principle, double and triple relativity and…
In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the…
We calculate the homology of three families of 2-step nilpotent Lie (super)algebras associated with the symplectic, orthogonal, and general linear groups. The symplectic case was considered by Getzler and the main motivation for this work…
A pair of uncertainty relations relevant for quantum states of multislit interferometry is derived, based on the mutually commuting "modular" position and momentum operators and their complementary counterparts, originally introduced by…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
We show that the quantum mechanical momentum and angular momentum operators are fixed by the Noether theorem for the classical Hamiltonian field theory we proposed.
In this paper we first prove a number of important inequalities with explicit constants in the setting of the Heisenberg group. This includes the fractional and integer Sobolev, Gagliardo-Nirenberg, (weighted) Hardy-Sobolev, Nash…
The unitary irreducible representations of a Lie group defines the Hilbert space on which the representations act. If this Lie group is a physical quantum dynamical symmetry group, this Hilbert space is identified with the physical quantum…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
We study the Lie point symmetries of semilinear Kohn-Laplace equations on the Heisenberg group H^1 and obtain a complete group classification of these equations.
We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups,…
We survey a few results on the boundedness of operators arising from the Weyl-Pedersen calculus associated with irreducible representations of nilpotent Lie groups.
We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
We show that generalised time-frequency shifts on the Heisenberg group $\mathbf{H}_n \cong \mathbb{R}^{2n+1}$, realised as a unitary irreducible representation of a nilpotent Lie group acting on $L^{2}(\mathbf{H}_n)$, give rise to a novel…
We approach uncertainty principles of Cowling-Price-Heis-\\enberg-type as a variational principle on modulation spaces. In our discussion we are naturally led to compact localization operators with symbols in modulation spaces. The optimal…
We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…
We introduce a special class of nilpotent Lie groups of step 2, that generalizes the so called $H$(eisenberg)-type groups, defined by A. Kaplan in 1980. We change the presence of inner product to an arbitrary scalar product and relate the…