We describe the deformed covariant phase space corresponding to the so-called κ-deformation of D = 4 relativistic symmetries, with quantum “time” coordinate and Heisenberg algebra obtained according to the Heisenberg double construction. The associated modified uncertainty relations are analyzed, and in particular it is shown that these relations are consistent with independent estimates of qua...

The aim of this paper is to generalize the q-Heisenberg uncertainty principles studied by Bettaibi et al. 2007, to state local uncertainty principles for the q-Fourier-cosine, the q-Fourier-sine, and the q-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the q-Bessel-Fourier transform.

The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder–Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with G...

Obtaining ground states of Hamiltonians is important in the condensed matter physics and quantum chemistry. The interaction typically contain not only diagonal but also off-diagonal elements. Although annealing provides a way to obtain state Hamiltonian, we can use Hamiltonian with Ising by using currently available commercial devices. In this work, propose for XXZ model, which contains both en...

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group N , there is a one-to-one correspondence between the set of isomorphism classes of connected Lie groups which are locally isomorphic to N and a union of certain quotients of noncompact Riemannian symmetric spaces.

Abstract. The Heisenberg group is one of the simplest sub-Riemannian settings in which we can define non-elliptic Hörmander type generators. We can then consider coercive inequalities associated to such generators. We prove that a certain class of nontrivial Gibbs measures with quadratic interaction potential on an infinite product of Heisenberg groups satisfy logarithmic Sobolev inequalities.

In the present paper we will characterize the continuous distributional solutions of Burgers’ equation such as those which induce intrinsic regular graphs in the first Heisenberg group H ≡ R, endowed with a leftinvariant metric d∞ equivalent to its CarnotCarathéodory metric. We will also extend the characterization to higher Heisenberg groups H ≡ R.

The Lieb-Schultz-Mattis theorem is extended to generalized Heisenberg models related to unexceptional Lie algebras. It is shown that there are no energy gaps above the ground states for SO(4), Sp(2), and SU(4) Heisenberg models; but gaps are suspected to occur in SO(5) and SO(6) models. The nondegenerate ground state for these models is rigorously proven.

Representations of the twisted Heisenberg-Virasoro algebra at level zero. Abstract. We describe the structure of the irreducible highest weight modules for the twisted Heisenberg-Virasoro Lie algebra at level zero. We prove that such a module is either isomorphic to a Verma module or to a quotient of two Verma modules.