Abstract
Weyl proposed a geometry that differed from Riemannian geometry, which underlies general relativity, in that it contained a vector that could be interpreted as describing the electromagnetic field. Dirac modified this geometry to remove certain difficulties and based it on a variational principle which gave satisfactory field equations for gravitation and electromagnetism. However, by changing the value of a parameter appearing in his variational principle one gets, instead of electromagnetism, a field of massive particles of spin 1, which can be assumed to interact with ordinary matter only through gravitation. It is suggested that these bosons, called weylons, provide most of the dark matter in the universe.
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References
A. Einstein,Ann. Phys. (Leipzig) 49, 769 (1916).
H. Weyl,Ann. Phys. (Leipzig) 59, 101 (1919).
P. A. M. Dirac,Proc. R. Soc. London 333, 403 (1973).
N. Rosen,Found. Phys. 12, 213 (1982).
A. L. Proca,J. Phys. Red. 7, 347 (1936).
M. S. Turner, Preprint (Fermilab-Conf. 91/78-A).
J. H. Jeans,The Dynamical Theory of Gases, 4th edn. (Cambridge University Press, London, 1925), p. 114.
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products (Academic New York, 1980), p. 322.
G. N. Watson,Theory of Bessel Functions (Cambridge University Press, Cambridge, 1944), pp. 79, 80.
Z. X. Wang and D. R. Guo,Special Functions (World Scientific, Singapore, 1989), p. 380.
E. Fischbachet al., Phys. Rev. Lett. 56, 3 (1986).
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Israelit, M., Rosen, N. Weyl-Dirac geometry and dark matter. Found Phys 22, 555–568 (1992). https://doi.org/10.1007/BF00732923
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DOI: https://doi.org/10.1007/BF00732923