Differential geometry, fiber bundles and physical theories
DOI: 10.1063/1.2914967
Among intellectual disciplines, mathematics occupies a unique position. It is in many respects an art, but it is also the language of science. Although a great deal of mathematics can be traced directly to external influences, much of its creativity is motivated internally: “pour la gloire de l’esprit humain,” as Carl G. T. Jacobi put it. Often the mathematician lets the imagination soar, constrained only by logic, intrinsic structure, and a sense of historical continuity. Yet from time to time these abstract deliberations have important applications in other fields.
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References
1. A general reference for fiber bundles and gauge theories is W. Drechsler, M. E. Mayer, Fiber‐Bundle Techniques in Gauge Theories, Lecture Notes in Physics volume 67, Springer, Berlin (1977).
2. For a review of self‐dual solutions see M. F. Atiyah, Geometry of Yang‐Mills Fields, Fermi Lectures 1979, Academia Nationale dei Lincei, Scuola Normale Superiore, Pisa (1979).
3. For a review of the twistor program see R. Penrose, Rep. Math. Phys. 12, 65 (1977).https://doi.org/RMHPBE
More about the authors
Isadore M. Singer, University of California, Berkeley.
