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The Universal Coefficient Theorem and Quantum Field Theory pp 1–15Cite as

Introduction

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Abstract

The current understanding of high energy physics represents a vast development even with respect to what was known in the same field 50 years ago. However, its fundamentals still lie mostly in perturbation theory, an idea that appeared much earlier in the context of astronomy and astrophysics [1–5]. Most of the present predictions of quantum electrodynamics rely on the fact that the coupling constant of this theory can be considered to be small and can be used as a perturbative expansion parameter. For other theories however, like quantum chromodynamics, the coupling constant is sufficiently small only in the high energy domain. In order to predict results for the low energy region one cannot directly rely on perturbation theory in the coupling constant anymore. Therefore non-perturbative techniques become relevant. These can be divided into two sections: numerical, lattice based methods on one side and analytic methods on the other side.

‘Begin at the beginning’, the King said, very gravely, ‘and go on till you come to the end: then stop.’

Lewis Carroll, Alice in Wonderland

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References

  1. J.C. Adams, On the perturbations of Uranus, UK Nautical Almanac Office, p. 265 (1851)

    Google Scholar 

  2. P.S. Marquis de Laplace, Theorie du mouvement et de la figure elliptique des planetes, Imprimerie de Ph. D. Pierres (1784)

    Google Scholar 

  3. Oeuvres completes de Laplace, vol 14. Paris Gauthier-Villars (1878–1912)

    Google Scholar 

  4. I. Newton, The mathematical papers of I. Newton (Cambridge University Press, Cambridge (1967–1981), p. 1–8

    Google Scholar 

  5. V. Puiseux, Recherches sur les fonctions algebriques, J. Math. Pure Appl. 15, 365 (1850)

    Google Scholar 

  6. P.S. Marquis de Laplace, Traite de mecanique celeste, Paris Duprat (1799)

    Google Scholar 

  7. V. Jankelevitch, Philosophie premiere (Introduction a une philosophie du presque, Gallimard, Paris, 1950)

    Google Scholar 

  8. N. Kolmogorov, The general theory of dynamical systems and classical mechanics (Proceedings of the International Congress of Mathematicians, Amsterdam, 1954)

    Google Scholar 

  9. H. Poincare, Les methodes nouvelles de la mecanique celeste, vol. 3 (Blanchard, Paris, 1987)

    MATH  Google Scholar 

  10. I. Newton, Philosophiae Naturalis Principia Mathematica, S. Pepys, Reg. Soc. Praeses (1686)

    Google Scholar 

  11. G.F. Leibniz, Nova methodus pro maximis et minimis, itemque tangentibus, suae nec fractas, nec irrationales quantitates moratur, et singulare pro Illis calculi genus, Acta Eruditorum, p. 467 (1684)

    Google Scholar 

  12. G.F. Leibniz, De geometria recondita et analysi indivisibilium atque infinitorum, Acta Eruditorum, p. 292 (1686)

    Google Scholar 

  13. G.F. Leibniz, Supplementum geometriae dimensoriae, seu generalissima omnium tetragonismorum effectio per motum: similiterque multiplex constructio lineae ex data tangentium conditione, Acta Eruditorum, p. 385 (1693)

    Google Scholar 

  14. C. Huygens, Horologium Oscillatorium (Dawsons of Pall Mall, Paris, 1673)

    Google Scholar 

  15. Euclid of Alexandria, Elements, (approx 300 BCE)

    Google Scholar 

  16. B. Russell, A History of Western Philosophy (Simon and Schuster, New York, 1972)

    Google Scholar 

  17. Archimedes of Syracuse, The Palimpsest (historical manuscript, original was erased and overwritten, contains: “Stomachion”, “The Method of Mechanical Theorems” and “On Floating Bodies”, it is the first known manuscript dealing with infinitesimal objects and a theory similar to modern calculus)

    Google Scholar 

  18. Diophantus of Alexandria, Arithmetica

    Google Scholar 

  19. Aristotle of Stagira, Prior Analytics

    Google Scholar 

  20. I. Kant, Critique of Pure reason (Cambridge University Press, Cambridge, 1988). ISBN 978-052-165729-7

    Google Scholar 

  21. Aristotle of Stagira, Physics

    Google Scholar 

  22. A. Grothendieck, Inst. des Hautes Etudes Scientiques, Pub. Math. 29, 95 (1966)

    Google Scholar 

  23. A. Grothendieck, Sur quelques points d’algebre homologique. Tohoku Math. J. 2(9), 119 (1957)

    Google Scholar 

  24. S. Mac Lane, Homology, Classics in Mathematics (Springer, Berlin, 1995). ISBN 3-540-58662-8

    Google Scholar 

  25. S.I. Gelfand, Y. Manin, Methods of Homological Algebra, 2nd edn, Springer Monographs in Mathematics. (Springer, Berlin, 2003). ISBN 3-540-43583-2

    Google Scholar 

  26. A. Hatcher, Algebraic Topology (Cambridge University Press, Cambridge, 2002). ISBN 0-521-79160-X

    Google Scholar 

  27. S. Mac Lane, Selected Papers (Springer, Berlin, 1979). ISBN 978-1-4615-7833-8

    Google Scholar 

  28. J.P. May, A Concise Course in Algebraic Topology, Chicago Lectures in Mathematics Series (1999). ISBN-13: 978-0226511832

    Google Scholar 

  29. J.L. Kelley, General Topology, Graduate Texts in Mathematics (Van Nostrand, New York, 1975). ISBN-13: 978-0923891558

    Google Scholar 

  30. O. Pedersen, In Quest of Sacrobosco, J. Hist. Astronomy, 16, 175 (1985)

    Google Scholar 

  31. G. Galilei, Drawings of the Moon, Florence, Biblioteca Nazionale Centrale, Ms. Gal. 48, f.28r, (1609)

    Google Scholar 

  32. G. Galilei, Dialogo sopra i due massimi sistemi del mondo (1632)

    Google Scholar 

  33. J.C. Maxwell, A dynamical theory of the electromagnetic field, Philos. Trans. R. Soc. Lond. 155, 459 (1865)

    Google Scholar 

  34. P.J. Nahin, Maxwell’s grand unification, IEEE Spectr. 29(3), 45 (1992)

    Google Scholar 

  35. C. Moller, M.S. Plesset, Note on an approximation treatment for many electron systems, Phys. Rev. 46,618 (1934)

    Google Scholar 

  36. R.P. Feynman, Atomic theory of the \(\lambda \) Transition in Helium, Phys. Rev. 91, 1291 (1953)

    Google Scholar 

  37. R. Sachs, Relativity, Groups and Topology, Lectures delivered at Les Houches during the 1963 session of the Summer School of Theoretical Physics, University of Grenoble, Vol. 1 (1964)

    Google Scholar 

  38. T. Regge, J. A. Wheeler, Stability of a Schwarzschild Singularity, Phys. Rev. 108, 1063 (1957)

    Google Scholar 

  39. H.S.M. Coxeter, Regular Polytopes, 3rd edn. (Dover Publications, New York, 1973) ISBN 0-486-61480-8

    Google Scholar 

  40. O. Byer, F. Lazebnik, D.L. Smeltzer, Methods for Euclidean Geometry (Wiley, New York, 2010). ISBN 978-0-88385-763-2

    Google Scholar 

  41. F. Hausdorff, Grundzuge der Mengenlehre, Leipzig: Veit, (1914). ISBN 978-0-8284-0061-9

    Google Scholar 

  42. L. Euler, Meditationes circa singulare serierum genus, Opera Omnia, I(15), 217 (1775)

    Google Scholar 

  43. H. Poincare, Analysis Situs, Journal de l’Ecole Polytechnique, 2(1), 1 (1895)

    Google Scholar 

  44. N. Bourbaki, Topologie Generale 1–4 (Springer, Berlin, (1995). ISBN 978-3-642-61701-0

    Google Scholar 

  45. C. Levi Strauss, The Savage Mind, The Nature of Human Society Series, ISBN-10: 0226474844 (1963)

    Google Scholar 

  46. C. Levi Strauss, The structural study of myth, J. Amer. Folklore, 28, 428 (1955)

    Google Scholar 

  47. J.C. Baez, J. Dolan, Categorification, Contemp. Math. 230, American Mathematical Society, Providence, Rhode Island, p. 1 (1998)

    Google Scholar 

  48. G. t’ Hooft, Magnetic monopoles in unified gauge theories, Nuclear Physics B79, p. 276 (1974)

    Google Scholar 

  49. St. Pokorski, Gauge Field Theories (Cambridge University Press, Cambridge, 1987). ISBN 978-0521478168

    Google Scholar 

  50. R.A. Bertlmann, Anomalies in Quantum Field Theory (Oxford Science Publications, Oxford, 2001). ISBN-13: 978-0198507628

    Google Scholar 

  51. B. Odom, D. Hanneke, B. D’Urso, G. Gabrielse, New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron. Phys. Rev. Lett. 97, 030801 (2006)

    Article  ADS  Google Scholar 

  52. A. Grothendieck, J. Dieudonne, Elements de geometrie algebrique, Publ. Inst. des Hautes Etudes Scientifiques, 4 (1960)

    Google Scholar 

  53. S.A. Morris, Topology Without Tears, Online e-book (2007)

    Google Scholar 

  54. G. ’t Hooft, A planar diagram theory for strong interactions, Nuclear Physics B72, p. 461(1974)

    Google Scholar 

  55. C. Weibel, History of Homological Algebra, ed. I.M. James. (Elsevier, New York, 1999). ISBN 9780521559874

    Google Scholar 

  56. E. Betti, Sopra gli spazi di un numero qualunque di dimensioni, Ann. Mat. pura appl. 2/4, p. 140 (1871)

    Google Scholar 

  57. D. Hilbert, Uber die Theorie der algebraischen Formen, 1st edn. (Teubner, Leipzig, 1890)

    Google Scholar 

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  1. Department of Physics and Astronomy, University College London, London, UK

    Andrei-Tudor Patrascu

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Patrascu, AT. (2017). Introduction. In: The Universal Coefficient Theorem and Quantum Field Theory. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-46143-4_1

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