Related papers: From Quantum Field Theory to Quantum Mechanics
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…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
A new localization scheme for Klein-Gordon particle states is introduced in the form of general space and time operators. The definition of these operators is achieved by establishing a second quantum field in the momentum space of the…
Quantizing the transfer of energy and momentum between interacting particles, we obtain a quantum impulse equation and relations that the corresponding mechanical power, force and torque satisfy. In addition to the energy-frequency and…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum mechanics. The vacuum or random zero-point radiation field has been shown previously, using the…
This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
Working within the framework of Loop Quantum Gravity (LQG), we construct a set of three operators suitable for identifying coordinate-like quantities on a spin-network configuration. In doing so, we rely on known properties of operators for…
We consider hamiltonian models representing an arbitrary number of spin $1/2$ fermion quantum fields interacting through arbitrary processes of creation or annihilation of particles. The fields may be massive or massless. The interaction…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by…
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.