Related papers: Multicomplementary operators via finite Fourier tr…
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…
A systematic study of holomorphic gauge invariant operators in general $\mathcal{N}=1$ quiver gauge theories, with unitary gauge groups and bifundamental matter fields, was recently presented in [1]. For large ranks a simple counting…
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…
In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is…
A complete set of N+1 mutually unbiased bases (MUBs) forms a convex polytope in the N^2-1 dimensional space of NxN Hermitian matrices of unit trace. As a geometrical object such a polytope exists for all values of N, while it is unknown…
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special…
Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…
The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with…
We set out to build a framework for self-adjoint extension theory for powers of the Jacobi differential operator that does not make use of classical deficiency elements. Instead, we rely on simpler functions that capture the impact of these…
We prove the following two results relating real mutually unbiased bases and representations of finite groups of odd order. Let $q$ be a power of 2 and $r$ a positive integer. Then we can find a $q^{2r}\times q^{2r}$ real orthogonal matrix…
We introduce an algebra $\mathcal H$ consisting of difference-reflection operators and multiplication operators that can be considered as a $q=1$ analogue of Sahi's double affine Hecke algebra related to the affine root system of type…
We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…
We introduce a novel framework consisting of a class of algebraic structures that generalize one-dimensional monoidal systems into higher dimensions by defining per-axis composition operators subject to non-commutativity and a global…
While causal perturbation theory and lattice regularisation allow treatment of the ultraviolet divergences in qed, they do not resolve the issues of constructive field theory, or show the validity of qed except as a perturbation theory. I…
In our previous paper \cite{co1} we have shown that the theory of circulant matrices allows to recover the result that there exists $p+1$ Mutually Unbiased Bases in dimension $p$, $p$ being an arbitrary prime number. Two orthonormal bases…
Frames in a Hilbert space that are generated by operator orbits are vastly studied because of the applications in dynamic sampling and signal recovery. We demonstrate in this paper a representation theory for frames generated by operator…
The whole Hilbert state space of an n-qubit spin system can be divided into (n+1) state subspaces according to the angular momentum theory of quantum mechanics. Here it is shown that any unknown state in such a state subspace, whose…
We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters…
We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard…
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the…