Related papers: Fock Representations of Quantum Fields with Genera…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
Non-Fock representations of the canonical commutation relations modeled over an infinite-dimensional nuclear space are constructed in an explicit form. The example of the nuclear space of smooth real functions of rapid decrease results in…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the…
A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…
The quantum theory of U(1) connections admits a diffeomorphism invariant representation in which the electric flux through any surface is quantized. This representation is the analog of the representation of quantum SU(2) theory used in…
We adress the problem of Fock space representations of (free) multiplet component fiels encountered in supersymmetric quantum field theory insisting on positivity and causality. We look in detail on the scalar and Majorana components of the…
Quantum field theory in curved spacetimes suffers in general from an infinite ambiguity in the choice of Fock representation and associated vacuum. In cosmological backgrounds, the requirement of a unitary implementation of the field…
In the state-vector space for relativistic quantum fields a new set of basis vectors are introduced, which are taken to be eigenstates of the field operators themselves. The corresponding eigenvalues are then interpreted as representing…
The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum…
We present a straightforward yet comprehensive theoretical study of different quantum states emerging from a bi-modal beamsplitter when various input states interfere. Specifically, we analyze the output states for different combinations of…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
Collective operators that describe interaction of generic quantum system with discrete spectrum with a quantum field are investigated. These operators, considered as operators in the entangled Fock space (space generated by action of…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…
We give a pedagogical introduction to algebraic quantum field theory (AQFT), with the aim of explaining its key structures and features. Topics covered include: algebraic formulations of quantum theory and the GNS representation theorem,…
We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental representations: the denominators of rational $R$-matrices…
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…
An analysis of the state space in the BRST--quantization in the Schroedinger representation is performed on the basis of the results obtained earlier in the framework of the Fock space representation. It is shown that to get satisfactory…