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Projective geometry and special relativity
Author(s) -
Delphenich D.H.
Publication year - 2006
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200510179
Subject(s) - path integral formulation , gauge theory , formalism (music) , faddeev–popov ghost , general relativity , theoretical physics , gauge fixing , quantization (signal processing) , von neumann architecture , physics , brst quantization , abelian group , introduction to gauge theory , quantum , mathematical physics , mathematics , quantum mechanics , pure mathematics , gauge boson , art , musical , visual arts , algorithm
Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics.