Abstract
Geometric approaches to particle physics have opened up new perspectives and unifying insights. After a few historical remarks I discuss the essence of the concept of G-theory: a primordial symmetry acting on a manifold and on the fields defined on it. This is then illustrated by the finite-dimensional case of Kaluza-Klein theories and by the infinite-dimensional case of chiral anomalies in Yang-Mills theories. In the latter case, a new and unifying description of topological and global anomalies is obtained.
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Th. Kaluza, Sitz.Preuß.Akad.Wiss.Berlin, Math.Phys.Kl.(1921)966
O. Klein, Z.Physik 37 (1926) 895
A. Pais: “Subtle is the Lord..., The Life and Science of Albert Einstein”, Clarendon Press, Oxford (1982)
J.M. Souriau, Nuovo Cini. 30 (1963) 565
J. Rayski, Acta Phys. Pol. 27(1965)89
A. Trautmann, Rep. Math. Phys. 1 (1970) 29
see e.g. the review by J.M. Duff, B.E.W. Nilsson and C.N. Pope, Phys. Reports 130(1986)1
R. Coquereaux and A. Jadzcyk; “Riemannian Geometry, Fiber Bundles, Kaluza-Klein Theories and All That”; World Scientific, Lecture Notes in Physics (1988)
A. Heil, N.A. Papadopoulos, B. Reifenhäuser and F. Scheck; Nucl.Phys. B293(1987)445
A. Heil, N.A. Papadopoulos and F. Scheck; “Reduction mechanism for symmetric fields on an orbit bundle”, preprint MZ-TH/88-07, to be published
D.J. Gross and M.J. Perry; Nucl.Phys. B226(1983)29
R.D. Sorkin; Phys.Rev.Lett. 51(1983)87
D. Pollard; J. Phys. A16(1983)565
E.T. Newman, L. Tamburino and T. Unti; J. MathPhys. 4(1963)915; A. Taub and C.W. Misner; Zh.Eksp.Teor.Fiz. 55(1968)233; S.W. Hawking; Phys.Lett. A60(1977)81
A. Heil, N.A. Papadopoulos, B. Reifenhäuser and F. Scheck; Phys.Lett. B173(1986)149 and Nucl.Phys. B281(1987)426
A. Heil, A. Kersch, N.A. Papadopoulos, F. Scheck and H. Vogel; Journ.Geom. and Phys. 6(1989)237; A. Heil, A. Kersch, N.A. Papadopoulos, B. Reifenhäuser and F. Scheck, Ann. of Phys. (N.Y.), in print
A. Heil, A. Kersch, N.A. Papadopoulos, B. Reifenhäuser and F. Scheck, “Structure of the space of reducible connections for Yang-Mills theories”, subm. to Rev. in Math.Phys.
I.M. Singer, Soc. Mathématique de France, Astérisque (1985)323
M.F. Atiyah and I.M. Singer, Proc.Nat.Acad.Sci. (USA) 81(1984)2597
A. Kersch: “Anomalien im Rahmen des Indextheorems”, thesis, Mainz Jan.1990
E. Witten, Phys.Lett. B117(1982)324
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© 1990 Springer-Verlag
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Scheck, F. (1990). Geometric approaches to particle physics. In: Ciulli, S., Scheck, F., Thirring, W. (eds) Rigorous Methods in Particle Physics. Springer Tracts in Modern Physics, vol 119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0117565
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DOI: https://doi.org/10.1007/BFb0117565
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