Related papers: A non-associative quantum mechanics
The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that…
The symmetrized product for quantum mechanical observables is defined. It is seen as consisting of the ordinary multiplication and the application of the superoperator that orders the operators of coordinate and momentum. This superoperator…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators $X_i$ which…
It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.
Using the natural irreducible 8-dimensional representation and the two spin representations of the quantum group $U_q$(D$_4$) of D$_4$, we construct a quantum analogue of the split octonions and study its properties. We prove that the…
Aim of this paper is to show the possible significance, and usefulness, of various non-selfadjoint operators for suitable Observables in non relativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically,…
We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it…
A novel generalization of the Askey-Wilson algebra is presented and shown to be associated with coproducts in the quantum algebra $U_q(su(1,1))$. This algebra has 15 non-commuting generators given by $Q^{(A)}$, with $A\subset \{1,2,3,4\}$…
This paper presents some of the basic properties of conditioned observables in finite-dimensional quantum mechanics. We begin by defining the sequential product of quantum effects and use this to define the sequential product of two…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
This paper is devoted to octonions that are the eight-dimensional hypercomplex numbers characterized by multiplicative non-associativity. The decomposition of the product of three octonions with the conjugated central factor into the sum of…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct…
A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of…
Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…