Related papers: On angular momentum operator in quantum field theo…
The relations between $L^{\pm}$ operators and the generators in the quantum enveloping algebras are studied. The $L^{\pm}$ operators for $U_{q}A_{N}$ and $U_{q}G_{2}$ algebras are explicitly expressed by the generators as examples.
We present two novel solutions of real Hilbert state quaternionic quantum mechanics ($\mathbb H$QM). Firstly, we observe that the angular momentum operator admits two different classes of physically non-equivalent free particles. As a…
Generalized definitions for angular and linear momentum are given and shown to reduce to the ADM (at spatial infinity) definitions and the definitions at null infinity in the appropriate limit. These definitions are used to express angular…
A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
Using a position operator obtained for spin 1 particles by the present author and Wigner, we obtain a quantum relativistic result for the hidden momentum force experienced by particles with structure. In particular, our result applies to…
We derive the effective angular momentum operator to $1/m^2$ and one-loop order in non-relativistic quantum electrodynamics (NRQED). In both dimensional and three-momentum-cutoff regularization schemes, we obtain the non-relativistic…
The individual parts of the total angular momentum operator in interacting theories cannot satisfy the canonical angular momentum commutation rule, including those proposed in the above paper. Furthermore, the operators in the new proposal…
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…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
Inspired by a similar, more general treatment by Kahler, we obtain the spin operator by pulling to the Cartesian coordinate system the azimuthal partial derivative of differential forms. At this point, no unit imaginary enters the picture,…
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.
The magnitude of the angular momentum ($J^2$) in quantum mechanics is larger than expected from a classical model. We explain this deviation in terms of quantum fluctuations. A standard quantum mechanical calculation gives the correct…
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the…
There are several definitions of the notion of angular momentum in general relativity. However non of them can be said to capture the physical notion of intrinsic angular momentum of the sources in the presence of gravitational radiation.…
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…
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 point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…