Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
31 (1990), S. 55-60
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A three-dimensional space-time geometry of relativistic particles is constructed within the framework of the little groups of the Poincaré group. Since the little group for a massive particle is the three-dimensional rotation group, its relevant geometry is a sphere. For massless particles and massive particles in the infinite-momentum limit, it is shown that the geometry is that of a cylinder and a two-dimensional plane. The geometry of a massive particle continuously becomes that of a massless particle as the momentum/mass becomes large. The geometry of relativistic extended particles is also considered. It is shown that the cylindrical geometry leads to the concept of gauge transformations, while the two-dimensional Euclidean geometry leads to a deeper understanding of the Lorentz condition.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528827
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