Related papers: Quantum Mechanical Effects from Deformation Theory
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
The ontology emerging from quantum field theory and the results following from Bell's theorems allowed the development of an intuitive picture of the microscopic world described by quantum mechanics, that is, we can say that we understand…
Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
We show that quantum particles constrained to move along curves undergoing cyclic deformations acquire, in general, geometric phases. We treat explicitly an example, involving particular deformations of a circle, and ponder on potential…
As revealed by space-time probing, mechanics and field theory come out as complementary descriptions for motions in space-time. In particular, quantum fields exert a radiation pressure on scatterers which results in mechanical effects that…
The concept of $q$-deformation, or ``$q$-analogue'' arises in many areas of mathematics. In algebra and representation theory, it is the origin of quantum groups; $q$-deformations are important for knot invariants, combinatorial…
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…
We present a theory of quantized radiation fields described in terms of q-deformed harmonic oscillators. The creation and annihilation operators satisfy deformed commutation relations and the Fock space of states is constructed in this…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
Based on some results on reparmetrisation of time in Hamiltonian path integral formalism, a pseudo time formulation of operator formalism of quantum mechanics is presented. Relation of reparametrisation of time in quantum with super…
We summarize our recently proposed approach to quantum field theory on noncommutative curved spacetimes. We make use of the Drinfel'd twist deformed differential geometry of Julius Wess and his group in order to define an action functional…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
We construct a q-deformed version of the conformal quantum mechanics model of de Alfaro, Fubini and Furlan for which the deformation parameter is complex and the unitary time evolution of the system is preserved. We also study differential…
We propose an approach to the quantum-classical correspondence based on a deformation of the momentum and kinetic operators of quantum mechanics. Making use of the factorization method, we construct classical versions of the momentum and…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…