Abstract
Compactified Minkowski spacetime is suggested by conformal covariance of Maxwell equations, while E. Cartan's definition of simple spinors leads to the idea of compactified momentum space. Assuming both diffeomorphic to (S 3 × S 1 )/Z 2 , one may obtain in the conformally flat stereographic projection field theories both infrared and ultraviolet regularized. On the compact manifold themselves instead, Fourier integrals of wave-field oscillations would have to be replaced by Fourier series summed over indices of spherical eigenfunctions: n, l, m, m′. Tentatively identifying those wave structures with spacetime itself (in the frame of Big-Bang) and/or with matter and radiation distribution, some large-scale (hydrogenic) and small-scale (lattice) space structures are conjectured.
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References
E. Cunningham,Proc. London Math. Soc. 8, 77 (1909); H. Bateman,Proc. London Math. Soc. 8, 223 (1909).
R. Penrose and W. Rindler,Spinors and Spacetime (Cambridge, University Press, Cambridge, 1986).
E. Cartan,Leçons sur la théorie des spineurs (Hermann, Paris, 1937).
P. Budinich, “Simple spinors and null momentum space,” I.L. SISSA Preprint (1992); P. Budinich and R. Raczka, “Global properties of conformally flat momentum space and their implications,” I.L. SISSA Preprint (1992).
P. Budinich and A. Trautman,The Spinorial Chessboard (Trieste Notes in Physics) (Springer, New York, 1988).
F. Reese Harvey,Spinors and Calibrations (Perspectives in Mathematics) (Academic Press New York, 1990).
H. Blaine Lawson, Jr., and M. L. Michelson,Spin Geometry (Princeton University Press, Princeton, 1989).
M. Cahen, S. Gutt, and A. Trautman, “Spin structures on real projective quadrics,” preprint, 1992.
P. Budinich and A. Trautman,J. Math. Phys. 30, 2125 (1989).
P. Budinich,Symmetry in Nature, Vol. 141 (Scuola Normale Superiore, Pisa, 1989).
D. Hestenes,Spacetime Algebra (Gordon & Breach, New York, 1987).
P. Budinich, “Spinor multiplets and Klein quadrics,”The Running Seminar on Spinors, Letter No. 14, 1991.
A. O. Barut and G. L. Bornzin,J. Math. Phys. 15, 1000 (1974).
G. Mack and I. T. Todorov,Phys. Rev. D 8, 1764 (1973).
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Budinich, P. Conformal compacifications from spinor geometry. Found Phys 23, 949–963 (1993). https://doi.org/10.1007/BF01891517
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DOI: https://doi.org/10.1007/BF01891517