Related papers: On momentum operator in quantum field theory
Relations between two definitions of (total) angular momentum operator, as a generator of rotations and in the Lagrangian formalism, are explored in quantum field theory. Generally, these definitions result in different angular momentum…
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
The space, on which quantum field operators are given, is constructed in any theory, in which the usual product between test functions is substituted by the $\star$-product (the Moyal-type product). The important example of such a theory is…
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…
Relativistic dynamics with energy and momentum resricted to an anti-de-Sitter space is presented, specifically in the introduction of coordiate operators conjugate to such momenta. Definition of functions of these operators, their…
We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations.
Conserved operator quantities in quantum field theory can be defined via the Noether theorem in the Lagrangian formalism and as generators of some transformations. These definitions lead to generally different conserved operators which are…
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…
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…
The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…
Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the…
It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational…
We show that the quantum mechanical momentum and angular momentum operators are fixed by the Noether theorem for the classical Hamiltonian field theory we proposed.
Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…
All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open…
The theory of the free Maxwell field in two moving frames on the de Sitter spacetime is investigated pointing out that the conserved momentum and energy operators do not commute to each other. This leads us to consider new plane waves…
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or…
An angular momentum operator in loop quantum gravity is defined using spherically symmetric states as a non-rotating reference system. It can be diagonalized simultaneously with the area operator and has the familiar spectrum. The operator…