Related papers: Quantum Groups and Polymer Quantum Mechanics
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
A rather non-standard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation has gained some attention in recent years, due to its possible relation with Planck scale…
I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\psi\rangle$ and a (hidden) quantum state $|\phi\rangle$ (that lives in the same Hilbert space), such that the…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…
In this paper all deformations of the general linear group, subject to certain restrictions which in particular ensure a smooth passage to the Lie group limit, are obtained. Representations are given in terms of certains sets of creation…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat…
Polymer quantization is a non-standard representation of the quantum mechanics that inspired by loop quantum gravity. To study the associated statistical mechanics, one needs to find microstates' energies which are eigenvalues of the…
In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data…
Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables…
We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense,…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).
Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems. Their orthogonality weight functions consist of quantum dilogarithm functions,…