nLab Lorentz force

Idea

The Lorentz force is the force exerted on a particle that is charged under the electromagnetic field.

See relativistic particle for details.

Properties

In Kaluza-Klein compactifications

If one models the electromagnetic field via the Kaluza-Klein mechanism as a field of gravity on a fiber bundle, then trajectories of charged particles subject to the Lorentz force in the base space of that bundle are euivalently just geodesics on the total space, e.g. (Bleecker 81). An exposition of this fact is in (Bartlett 13).

Related concepts

• quantum Hall effect

• strong nuclear force

• weak nuclear force

References

Named after Hendrik Lorentz.

Textbook accounts:

• V. C. A. Ferraro, §303 in: Electromagnetic Theory, The Athlone Press (1954, 1956)

Discussion in worldline Lagrangian mechanics:

• Charles Misner, Kip Thorne, John Wheeler, Exc. 7.2 (p. 179) in: Gravitation, W. H. Freeman, San Francisco (1973) [ISBN:9780716703440]

• Theodore Frankel, §16.4b in: The Geometry of Physics - An Introduction, Cambridge University Press (1997, 2004, 2012) [doi:10.1017/CBO9781139061377]

See also

• Wikipedia, Lorentz force

On generalization to the spinning particle:

• Jan-Willem van Holten, Relativistic Dynamics of Spin in Strong External Fields [arXiv:hep-th/9303124]

Discussion of Lorentz force from the point of view of the Kaluza-Klein mechanism:

• David Bleecker, Gauge theory and variational principles, Dover publications, 1981.

and exposition is in

• Bruce Bartlett, The geometry of force, Sept 2013 (pdf).