Related papers: An algebraic analysis framework for quantum calcul…
Let $A$ be a commutative ring with unity and $B = A[\theta]$ be an integral extension of $A$. Assume that $B$ is an integral domain with quotient field $\mathbb{K}$ and $\mathbb{E}$ is the minimal splitting field of $\theta$ over…
This paper is a brief review of recent results on the concept of ``generalized $\tau$-function'', defined as a generating function of all the matrix elements in a given highest-weight representation of a universal enveloping algebra ${\cal…
This paper proposed a framework based on quantum computing for reliability assessment of complex systems. The 'Quantum Twin' concept was also proposed. The framework can be used to accelerate the reliability assessment of large-scale…
The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of topological strings and 5D SUSY gauge theories. The quantum…
The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…
Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion…
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…
To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term ${e}^{-itg(S_{+}\otimes a+S_{-}\otimes a^{\dagger})}$ explicitly which is very hard. In this paper we try to make the quantum matrix…
Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
A method is discussed to analyze the dynamics of a dissipative quantum system. The method hinges upon the definition of an alternative (time-dependent) product among the observables of the system. In the long time limit this yields a…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $ U(1) $ -covariance. Explicit representations of possible $q $-Lie algebras are constructed…
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after…
This article is concerned with obtaining the standard tau function descriptions of integrable equations (in particular, here the KdV and Ernst equations are considered) from the geometry of their twistor correspondences. In particular, we…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
A theoretical framework based on a simple quasi-number algebra is investigated in a treatment of space-time and gravity.
It is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian H=\half p^2+\half\mu^2x^2-\lambda x^4 in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…