Related papers: Tensor operators and Wigner-Eckart theorem for U_q…
In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well known Petrov classification emerging as a…
Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in…
The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a…
An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…
The three-particle operator in a second quantized form is studied. The operator is transformed into irreducible tensor form. Possible coupling schemes, distinguished by the classes of symmetric group \mathrm{S_{6}}, are presented.…
It is shown that the mixed states of a closed dynamics support a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are…
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…
Recent experimental advances in ultrafast science put different processes occurring on the electronic timescale below a few femtoseconds in focus. In the present theoretical work, we demonstrate how the transformation and propagation of the…
The transition from unitary, reversible von Neumann-Everett quantum processes to non-unitary, irreversible processes and measurements is explored through infinite tensor products interpreted as nested, chained, or iterated Wigner's friend…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
This paper aims to provide an introduction to a basic form of the ${\bf Q}$-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has…
The phase diagram of quantum electron bilayers in zero magnetic field is obtained using density functional theory. For large electron densities the system is in the liquid phase, while for smaller densities the liquid may freeze (Wigner…
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
We extend the quantum geometric tensor from the state space to the operator level,and investigate its properties like the additivity for factorizable models and the splitting of two kinds contributions for the case of stationary reference…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
We construct operator systems $\mathfrak C_I$ that are universal in the sense that all operator systems can be realized as their quotients. They satisfy the operator system lifting property. Without relying on the theorem by Kirchberg, we…
In this short note, we establish an operator theoretic version of the Wiener-Ikehara tauberian theorem, and point out how this leads to a new proof of the Prime number theorem that should be accessible to anyone with a basic knowledge of…
Operators play a substantial role in mathematical formalism of quantum mechanics. However, explicit forms of the operators are usually postulated, based on the intuitive assumptions. In this study, variational principle was applied to the…
An action of the $\mathfrak{sl}_2$-crystal category on graded/mixed (integral) category $\mathcal{O}$ `lifting' the usual tensor product is defined.