Related papers: The A-model with mutually equal model parameters c…

Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…

Starting from the coadjoint Poincar\'e algebra we construct a point particle relativistic model with an interpretation in terms of extra-dimensional variables. The starting coadjoint Poincar\'e algebra is able to induce a mechanism of…

Two-Higgs-doublet models come with an augmented parameter space which allows them to possibly solve some of the shortcomings of the Standard Model, and opens the window to a plethora of new phenomena to be discovered. The introduction of…

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

We compare the concept of triplet of closely embedded Hilbert spaces with that of generalised triplet of Hilbert spaces in the sense of Berezanskii by showing when they coincide, when they are different, and when starting from one of them…

A spin-space extension is reviewed, which provides information on the standard model. Its defining feature is a common matrix space that describes symmetries and representations, and leads to limits on these, for given dimension. The model…

Several examples and models based on noncommutative differential calculi on commutative algebras indicate that a metric should be regarded as an element of the left-linear tensor product of the space of 1-forms with itself. We show how the…

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries (J. Phys. A: Math. Theor. Vol. 42 (2009) 395202 (20pp)), mixed…

Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix…

The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing…

We discuss the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. We investigate which of the classical properties can be translated to this more general framework and the way in…

A model with three scalar doublets can be conveniently accommodated within an A4 symmetric framework. The A4 symmetry permits only a restricted form for the scalar potential. We show that for the global minima of this potential alignment…

We study expansions of Hilbert spaces with a bounded normal operator $T$. We axiomatize this theory in a natural language and identify all of its completions. We prove the definability of the adjoint $T^*$ and prove quantifier elimination…

We investigate the parameter space of the Inert Doublet Model, which is a straightforward extension of the SM in the scalar sector. We apply a set of constraints both from the theoretical and experimental side to extract and determine…

Necessary and sufficient conditions for a dense subspace of a Hilbert space to be a linear Hilbertian manifold domain are given. Some relations between linear Hilbertian manifold domains and domains of self-adjoint operators are found.

Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to…

In this short note we present a far generalization of the following very well-known assertion: assume that we have two orthonormal sequences in a Hilbert space and these sequences are quadratically close to each other. Then if one of these…

Superconducting quantum symmetries in extended single-band 1-dimensional Hubbard models are shown to originate from the classical (pseudo-)spin SO(4) symmetry of a class of models of which the standard Hubbard model is a special case.…

Open systems with non-Hermitian degeneracies called exceptional points show a significantly enhanced response to perturbations in terms of large energy splittings induced by a small perturbation. This reaction can be quantified by the…