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arXiv:quant-ph/0512162

Nonlocality I: Nonlocality, singularity, and elastic scattering in quantum fields

Hai-Jhun Wanng

Published Dec 20, 2005• 0 citations
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Abstract

Using path integrals we express the quantum nonlocality of AB-effect type in the form of singularity. The gauge-fixing term in path integrals induce the AB effect in ordinary scattering processes. This means that all scattering processes are accompanied by nonlocal effect. The formulae are then extended to theory of fields that additionally include a scalar potential. It turns out that the degree of freedom of nonlocality in quantum fields is just the degree of the ghosts. Furthermore, renormalization method can be related to this type of nonlocal effect.

DOI
10.48550/arxiv.quant-ph/0512162

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Using path integrals we express the quantum nonlocality of AB-effect type in the form of singularity. The gauge-fixing term in path integrals induce the AB effect in ordinary scattering processes. This means that all scattering processes are accompanied by nonlocal effect. The formulae are then extended to theory of fields that additionally include a scalar potential. It turns out that the degree of freedom of nonlocality in quantum fields is just the degree of the ghosts. Furthermore, renormalization method can be related to this type of nonlocal effect.
In the previous paper, it has been proved that elastic scattering processes of two quantum particles are always accompanied with nonlocal processes. Furthermore, it is found that setting an additional Hamiltonian after the originally scattering one can help to describe the two type of processes in a united frame. Here we discuss the contribution of this additional Hamiltonian to irreversible process in isolated quantum systems. The use of the Hamiltonian can induce the non-Markovian Langevin equation, showing a complex memory effect, and thus revealing the irreversible essence of isolated system without appealing to reservoir or approximate methods (e.g. coarse grain) as usually done.
When the electromagnetic potentials are expressed in the Coulomb gauge in terms of the electric and magnetic fields rather than the sources responsible for these fields they have a simple form that is nonlocal (i.e., the potentials depend on the fields at every point in space). It is this nonlocality of classical electrodynamics that is primarily responsible for the puzzle associated with the static Aharonov–Bohm effect: that its interference pattern is affected by fields in a region of space that the electron beam never enters.
This work introduces nonlocal corrections to gauge potentials arising when quantum paths traverse regions of nonzero electromagnetic field strength. These corrections restore single-valuedness of the gauge function and resolve inconsistencies that appear in standard treatments of phase accumulation when paths cross field regions. Explicit analytic expressions are derived for static and time-dependent configurations, including solvable stripe models. The results suggest a geometric path dependence beyond conventional formulations of gauge phases and may have implications for the Aharonov–Bohm effect, Berry phases, and related gauge-theoretic constructions. This manuscript represents the first part of a broader investigation of nonlocal gauge corrections and their physical applications.
The effective-mass method for treating scattering by nonlocal potentials described in a previous publication. is applied to some problems in atomic collision theory. The applications are based on an effective equation for scattering in the elastic channel when coupling with other channels is included, giving rise to a nonlocal effective potential. We use the effective-mass theory to analyze the influence of coupling with closed channels on the elastic scattering in atom-atom collisions and point out that this may lead to a new type of rainbow effect. We show that strong interchannel coupling results in the appearance of poles and zeros in the effective mass and that the latter may lead to compound-state resonances and orbiting effects. It is observed that the occurences of Fesbach resonances in molecular encounters is always reflected in the presence of zeroes in the corresponding effective mass. We also employ the effective-mass method to deal briefly with the familiar problem of curve crossing and nonadiabatic transitions in atomic collisions.