Related papers: A nonassociative operator decomposition of strongl…
The unmodified Heisenberg-Pauli canonical formalism of quantum field theory applied to a self-interacting scalar boson field is shown to make sense mathematically in a framework of generalized functions adapted to nonlinear operations. The…
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".
The formalism of quantum field theory in operator form, based on the anti self-adjoint operators of the imaginary coordinate and momentum and the self-adjoint operators of the real coordinate, momentum, energy and time, is used in…
This work gives value to the importance of Hilbert-Schmidt operators in the formulation of a noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework.
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…
In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals…
In this paper we study a system of $N$ coupled quantum oscillators interacting with each other directly with varying coupling strengths and indirectly through linear couplings to a scalar massless quantum field as its environment. The…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
A new approach to constructing the noncommutative scalar field theory is presented. Not only between x_i and p_j, we impose commutation relations between x_is as well as p_js, and give a new representation of x_i,p_js. We carry out both…
It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
Non-manifest symmetries are an important feature of quantum field theories (QFTs), and yet their characteristics are not fully understood. In particular, the construction of the charge operators associated with these symmetries is…
Well-defined nonlinear deformations of free quantum fields are introduced as manifestly Poincar\'e invariant scaling and resonance properties of non-dynamical scale models in Minkowski space, instead of introducing nonlinear dynamical…
Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which…
An axiomatic quantum field theory applied to the self-interacting boson field is realised in terms of generalised operators that allows us to form products and take derivatives of the fields in simple and mathematically rigorous ways.…
Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie…
We revisit Wigner's question about the admissible commutation relations for coordinate and velocity operators given their equations of motion (EOM). In more general terms we want to consider the question of how to quantize dynamically…
Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because a new formulation can be given to…