Potential Operators

Paul Cooney

Paper IV — Local Interactions and Potentials from Operational Locality DescriptionThis paper shows how local interaction terms and effective potentials arise from operational locality constraints. By analyzing admissible deformations of free ordered dynamics, we derive interaction structure without invoking classical force laws or background geometry. The results clarify why local potentials dominate physical dynamics and how interaction terms reflect operationally constrained information exchange. Keywordslocal interactions; emergent potentials; operational physics; quantum dynamics; reconstruction theory; locality

Jochen Pade

A. W. Saénz, W. W. Zachary

In a previous paper, we have proposed a definition of wave operators for hard-core potentials of long range from the standpoint of time-dependent single-channel quantum scattering theory. In the present note, we prove the existence of these operators for a large class of such potentials. The proof involves a combination of methods previously used to establich the existence of wave operators for short-range hard-core potentials and long-range potentials without hard cores.

Pieter Kok

Tadahiro Miyao

Considered is a quantum system of $N(\ge2)$ charged particles moving in the plane ${\mathbb R}^2$ under the influence of a perpendicular magnetic field concenrated on the positions where the particle exsists. The gauge potential which gives this magnetic field is called a winding gauge potential. Properties of the momentum operators with a winding gauge potential are investigated. The momentum operators with a winding gauge potential are represented by the fibre direct integral of Arai's momentum operators [1]. Using this fibre direct integral decomposition, commutation properties of the momentum operators are investigated. A notion of local quantization of the magnetic flux is introduced to characterize the strong commutativity of the momentum operators. Aspects of the representation of the canonical commutation relations (CCR) are discussed. There is an interesting relation between the representation of the CCR with respect to this system and Arai's representation. Some applications of those results are also discussed.

Belal Ehsan Baaquie