Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the no...

Non-highest weight representations of the current algebra so(1, n), and Laplace Operators. Abstract We constructed canonical non-highest weight unitary irreducible representation of so(1, n) current algebra as well as canonical non-highest weight non-unitary representations, We constructed certain Laplacian operators as elements of the universal enveloping algebra, acting in representation spac...

It is fundamental to view unitary braiding operators describing topological entangle-ments as universal quantum gates for quantum computation. This paper derives a unitary solution of the quantum Yang–Baxter equation via Yang–Baxterization and constructs the Hamiltonian responsible for the time-evolution of the unitary braiding operator.

We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer science. We conclude that either the Church-Turing thesis needs revision, or that only restricted classes of observables may be realized, in principle, as measureme...

On one-dimensional two-way infinite quantum lattice system, a property of translationally invariant stationary states with nonvanishing current expectation is investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show that spectrum of the unitary operators, energy-momentum spectrum with respect to the ...