Abstract
The first part of the 20th century saw the most revolutionary breakthroughs in the history of theoretical physics, the birth of general relativity and quantum field theory. The seemingly nearly completed description of our world by means of classical field theories in a simple Euclidean geometrical setting experienced major modifications: Euclidean geometry was abandoned in favor of Riemannian geometry, and the classical field theories had to be quantized. These ideas gave rise to today’s theory of gravitation and the standard model of elementary particles, which describe nature better than anything physicists ever had at hand. The dramatically large number of successful predictions of both theories is accompanied by an equally dramatically large number of problems.
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References
1. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Boulder 1995)
2. S. Weinberg, The Quantum Theory Of Fields, Vols. I, II, and III, (Cambridge University Press, Cambridge 1995, 1996, and 2000)
3. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 4th edn. (Carendon Press, Oxford 2002)
4. R. Wald, General Relativity (The University of Chicago Press, Chicago 1984)
5. S. Weinberg, Gravitation and Cosmology (Wiley, New York 1972)
6. R. A. Bertlmann, Anomalies in Quantum Field Theory (Oxford University Press, Oxford 1996)
7. S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge 1985)
8. H. Forkel, A Primer on Instantons in QCD, ar**v:hep-ph/0009136
9. R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam 1982)
10. M. Göckeler and T. Schücker, Differential Geometry, Gauge Theories, and Gravity (Cambridge University Press, Cambridge 1987)
11. M. Nakahara, Geometry, Topology and Physics, 2nd ed. (IOP Publishing, Bristol 2003)
12. C. Nash and S. Sen, Topology and Geometry for Physicists (Academic Press, London 1983)
13. B. F. Schutz, Geometrical Methods of Mathematical Physics (Cambridge University Press, Cambridge 1980)
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Bick, E., Steffen, F. Introduction and Overview. In: Bick, E., Steffen, F.D. (eds) Topology and Geometry in Physics. Lecture Notes in Physics, vol 659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31532-2_1
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DOI: https://doi.org/10.1007/978-3-540-31532-2_1
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