Related papers: On the structure of covariant phase observables
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
The baryon structure is investigated in a covariant diquark-quark model. In this approach baryons emerge as relativistic bound states of a constituent quark and a $0^{+}$ or $1^{+}$ diquark. After solving the Bethe-Salpeter Equation for the…
In this work, we propose to apply the recently developed Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant…
We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
The conditions under which a given manifold $M$ may be given a tangent bundle or a cotangent bundle structure are analyzed. This is an important property arising in different contexts. For instance, in the study of integrability of a given…
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…
The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich-Weyl…
We will give a new model for measurements of a quantum system such that the measuring apparatuses are described by a unital separable non-type I nuclear simple C$^*$-algebra equipped with certain unital endomorphisms and pure states. An…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
We derive an estimate of statistical error in calculating the trace of a large matrix by using random vector, and show that {\em random phase vector} gives the results with the smallest statistical error for a given basis set. This result…
Within the framework of supersymmetric quantum mechanics, we study the simplified version of potential algebra of shape invariance condition in k steps, where k is an arbitrary positive integer. The associated potential algebra is found to…
We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…