The nonrelativistic formulation is traditionally given in terms of particle paths, not fields.
2.
In a microtron, due to the electrons'increasing momentum, the particle paths are different for each pass.
3.
In a moving vortex, the particle paths are not closed, but are open, loopy curves like solenoidal.
4.
The tracker needs to record particle paths accurately yet be lightweight so as to disturb the particle as little as possible.
5.
The field representation is a sum over all field configurations, and the particle representation is a sum over different particle paths.
6.
The path integral in this case is the analog of a sum over particle paths, not of a sum over field configurations.
7.
A Feynman diagram is a contribution of a particular class of particle paths, which join and split as described by the diagram.
8.
Nevertheless, an analysis of the theoretical justification of the space-time approach shows that its success does not imply that particle paths need be taken seriously.
9.
It is used in the calculation of particle paths in circular particle accelerators ( like synchrotrons ), and for astronomical objects that are bound by gravitation.
10.
We've learned to go from the ray tracing of the trajectories or particle paths of the classical mechanics of the 19th century to the wave mechanics of the 20th century.
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