Related papers: The Wigner-Eckart Theorem for Reducible Symmetric …
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…
The Wigner derivative is the partial derivative of dihedral angle with respect to opposite edge length in a tetrahedron, all other edge lengths remaining fixed. We compute the inverse Wigner derivative for spherical tetrahedra, namely the…
In this paper we introduce a new method to produce lower bounds for the Waring rank of symmetric tensors. We also introduce the notion of $e$-computability and we use it to prove that Strassen's Conjecture holds in infinitely many new…
Using the complete orthonormal sets of radial parts of nonrelativitistic exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical harmonics of rank s the new formulae for the 2(2s+1)-component relativistic spinors…
In this paper, we will show that for an operator $T$ which is injective and has dense range, there exists an invertible operator $X$ (in fact we can find $U+K$, where $U$ is an unitary operator and $K$ is a compact operator with norm less…
We present an operator algebraic approach to Wigner's unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert…
A well-known theorem due to R. E. Curto and N. Salinas gives a necessary and sufficient condition for the unitary equivalence of commuting tuples of bounded linear operators acting on reproducing kernel Hilbert spaces. Inspired by this…
We systematically derive a linear quantum collision operator for the spinorial Wigner transport equation from the dynamics of a composite quantum system. For suitable two particle interaction potentials, the particular matrix form of the…
Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
Biquadratic tensors play a central role in many areas of science. Examples include elasticity tensor and Eshelby tensor in solid mechanics, and Riemann curvature tensor in relativity theory. The singular values and spectral norm of a…
This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the…
We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…