Related papers: Relativity implications of the quantum phase
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
We describe a categorical model of MALL (Multiplicative Additive Linear Logic) inspired by the Heisenberg-Schr\"odinger duality of finite-dimensional quantum theory. Proofs of formulas with positive logical polarity correspond to CPTP…
We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated…
The definition of invariant time is fundamental to relativistic symmetry. Invariant time may be formulated as a degenerate orthogonal metric on a flat phase space with time, position, energy and momentum degrees of freedom that is also…
This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
This is an expositary article telling a short story made from the leaves of quantum probability with the following ingredients: (i) A special projective, unitary, irreducible and factorizable representation of the euclidean group of a…
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…
The observable algebra O of SO_q(3)-symmetric quantum mechanics is generated by the coordinates of momentum and position spaces (which are both isomorphic to the SO_q(3)-covariant real quantum space R_q^3). Their interrelations are…
The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz…
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…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…
We provide a homological model for a family of quantum representations of mapping class groups arising from non-semisimple TQFTs (Topological Quantum Field Theories). Our approach gives a new geometric point of view on these…
Following the method of induced group representations of Wigner-Mackay, the explicit construction of all the unitary irreducible representations of the discrete finite Heisenberg-Weyl group $HW_{2^s}$ over the discrete phase space lattice…
A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the…
The Weyl algebra (W_{2m}[h]; *) is the algebra generated by u=(u_1,...,u_m,v_1,.....,v_m) over C with the fundamental commutation relation [u_i,v_j]=-ih\delta_{ij}, where h is a positive constant. The Heisenberg algebra (\Cal H_{2m}[nu];*)…
We consider quantum mechanics on the noncommutative spaces characterized by the commutation relations $$ [x_a, x_b] \ =\ i\theta f_{abc} x_c\,, $$ where $f_{abc}$ are the structure constants of a Lie algebra. We note that this problem can…
We consider a special category of Hopf algebras, depending on parameters $\Sigma$ which possess properties similar to the category of representations of simple Lie group with highest weight $\lambda$. We connect quantum groups to minimal…