Related papers: Deformed classical-quantum mechanics transition
We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the…
In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
On the basis of the quantum q-oscillator algebra in the framework of quantum groups and non-commutative q-differential calculus, we investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized…
In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…
A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
We perform a deformation quantization of the classical isotropic rigid rotator. The resulting quantum system is not invariant under the usual $SU(2)\times SU(2)$ chiral symmetry, but instead $SU_{q^{-1}}(2) \times SU_q(2)$.
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…