Annales Henri Poincaré

, Volume 19, Issue 3, pp 843–874 | Cite as

The Chirality Theorem

  • José M. Gracia-Bondía
  • Jens MundEmail author
  • Joseph C. Várilly


We show how chirality of the weak interactions stems from string independence in the string-local formalism of quantum field theory.

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  1. 1.
    Socrates: “Would a sensible husbandman, who has seeds which he cares for and which he wishes to bear fruit, plant them with serious purpose in the heat of summer in some garden of Adonis...?”Google Scholar
  2. 2.
    Quigg, C.: Unanswered questions in the electroweak theory. Ann. Rev. Nucl. Part. Sci. 59, 505–555 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    Lynn, B. W., and Starkman, G. D.: Global \(SU(3)_C \times SU(2)_L \times U(1)_Y\) linear sigma model with Standard Model fermions: axial-vector Ward Takahashi identities, the absence of Brout–Englert–Higgs mass fine tuning, and the decoupling of certain heavy particles, due to the Goldstone theorem. arXiv:1509.06199
  4. 4.
    Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Addison-Wesley, Reading (1995)Google Scholar
  5. 5.
    Marshak, R.E.: Conceptual Foundations of Modern Particle Physics. World Scientific, Singapore (1993)CrossRefGoogle Scholar
  6. 6.
    Mund, J., Schroer, B., Yngvason, J.: String-localized quantum fields from Wigner representations. Phys. Lett. B 596, 156–162 (2004)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Mund, J., Schroer, B., Yngvason, J.: String-localized quantum fields and modular localization. Commun. Math. Phys. 268, 621–672 (2006)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Mandelstam, S.: Quantum electrodynamics without potentials. Ann. Phys. (NY) 19, 1–24 (1962)ADSCrossRefzbMATHGoogle Scholar
  9. 9.
    Steinmann, O.: Perturbative QED in terms of gauge invariant fields. Ann. Phys. (NY) 157, 232–254 (1984)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Schroer, B.: Beyond gauge theory: positivity and causal localization in the presence of vector mesons. Eur. Phys. J. C 76, 378 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    Weinberg, S.: The Quantum Theory of Fields I. Cambridge University Press, Cambridge (1995)CrossRefGoogle Scholar
  12. 12.
    Nikolov, N.M., Stora, R., Todorov, I.: Renormalization of massless Feynman amplitudes in configuration space. Rev. Math. Phys. 26, 1430002 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Várilly, J.C., Gracia-Bondía, J.M.: Stora’s fine notion of divergent amplitudes. Nucl. Phys. B 912, 28–37 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Wigner, E.P.: On unitary representations of the inhomogeneous Lorentz group. Ann. Math. 40, 149–204 (1939)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Yngvason, J.: Zero-mass infinite spin representations of the Poincaré group and quantum field theory. Commun. Math. Phys. 18, 195–203 (1970)ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    Iverson, G.J., Mack, G.: Quantum fields and interactions of massless particles: the continuous spin case. Ann. Phys. (NY) 64, 211–253 (1971)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Rehren, K.-H.: Pauli–Lubanski limit and stress-energy tensor for infinite-spin fields. JHEP 1711, 130–164 (2017)Google Scholar
  18. 18.
    Peskin, M.: Standard Model and symmetry breaking. Talk given at the Latin American conference on High Energy Physics: Particles and Strings II, Havana (2016)Google Scholar
  19. 19.
    Dütsch, M., Scharf, G.: Perturbative gauge invariance: the electroweak theory. Ann. Phys. (Leipzig) 8, 359–387 (1999)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Aste, A., Scharf, G., Dütsch, M.: Perturbative gauge invariance: electroweak theory II. Ann. Phys. (Leipzig) 8, 389–404 (1999)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Scharf, G.: Gauge Field Theories: Spin One and Spin Two. Dover, Mineola (2016)Google Scholar
  22. 22.
    Stora, R.: From Koszul complexes to gauge fixing. In: ’t Hooft, G. (ed.) 50 Years of Yang-Mills Theory, pp. 137–167. World Scientific, Singapore (2005)Google Scholar
  23. 23.
    Mund, J.: String-localized quantum fields, modular localization, and gauge theories. In: Sidoravičius, V. (ed.) New Trends in Mathematical Physics, pp. 495–508. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Duch, P.: Massless fields and adiabatic limit in quantum field theory. Ph. D. thesis, Jagiellonian University, Cracow, summer 2017; arXiv:1709.09907
  25. 25.
    Leibbrandt, G.: Introduction to noncovariant gauges. Rev. Mod. Phys. 59, 1067–1119 (1987)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Figueiredo, F.: Lightlike string-localized free quantum fields for massive bosons. M. Sc. thesis, Universidade Federal de Juiz de Fora, (2017)Google Scholar
  27. 27.
    Plaschke, M., Yngvason, J.: Massless, string localized quantum fields for any helicity. J. Math. Phys. 53, 042301 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Mund, J., de Oliveira, E.T.: String-localized free vector and tensor potentials for massive particles with any spin: I. Bosons. Commun. Math. Phys. 355, 1243–1282 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Mund, J., Rehren, K.-H., Schroer, B.: Helicity decoupling in the massless limit of massive tensor fields. Nucl. Phys. B 924, 699–727 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Bogoliubov, N.N., Shirkov, D.V.: Introduction to the Theory of Quantized Fields, 3rd edn. Wiley, New York (1980)Google Scholar
  31. 31.
    Epstein, H., Glaser, V.: The role of locality in perturbation theory. Ann. Inst. Henri Poincaré A 19, 211–295 (1973)MathSciNetzbMATHGoogle Scholar
  32. 32.
    Schwartz, L.: Théorie des Distributions. Hermann, Paris (1966)zbMATHGoogle Scholar
  33. 33.
    Zichichi, A.L., et al.: Special section on symmetries and gauge invariance. In: Zichichi, A.L. (ed.) Gauge Interactions, pp. 725–740. Plenum Press, New York (1984)CrossRefGoogle Scholar
  34. 34.
    Okun, L.B.: From pions to wions. In The Relations of Particles, pp. 31–45. World Scientific, Singapore (1991)Google Scholar
  35. 35.
    Scheck, F.: Electroweak and Strong Interactions: Phenomenology, Concepts, Models. Springer, Berlin (2012)CrossRefGoogle Scholar
  36. 36.
    Nagashima, Y.: Elementary Particle Physics 2: Foundations of the Standard Model. Wiley, Singapore (2013)CrossRefzbMATHGoogle Scholar
  37. 37.
    Mund, J.: String-localized massive vector bosons in interaction. In preparationGoogle Scholar
  38. 38.
    Mund, J., Schroer, B.: How the Higgs potential got its shape. ForthcomingGoogle Scholar
  39. 39.
    Cornwall, J.M., Levin, D.N., Tiktopoulos, G.: Uniqueness of spontaneously broken gauge theories. Phys. Rev. Lett. 30, 1268–1270 (1973)ADSCrossRefGoogle Scholar
  40. 40.
    Cornwall, J.M., Levin, D.N., Tiktopoulos, G.: Derivation of gauge invariance from high-energy unitarity bounds on the S-matrix. Phys. Rev. D 10, 1145–1167 (1974)ADSCrossRefGoogle Scholar
  41. 41.
    Schwartz, M.D.: Quantum Field Theory and the Standard Model. Cambridge University Press, Cambridge (2014)Google Scholar
  42. 42.
    Thomas, L.J., Wichmann, E.H.: On the causal structure of Minkowski spacetime. J. Math. Phys. 38, 5044–5086 (1997)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Streater, R.F., Wightman, A.S.: PCT, Spin and Statistics, and All That. W. A. Benjamin, New York (1964)zbMATHGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • José M. Gracia-Bondía
    • 1
  • Jens Mund
    • 2
    Email author
  • Joseph C. Várilly
    • 3
  1. 1.Departamento de Física TeóricaUniversidad de ZaragozaZaragozaSpain
  2. 2.Departamento de FísicaUniversidade Federal de Juiz de ForaJuiz de ForaBrasil
  3. 3.Escuela de MatemáticaUniversidad de Costa RicaSan JoséCosta Rica

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