Non-Abelian Gauge Theories

  • Edouard B. Manoukian
Part of the Graduate Texts in Physics book series (GTP)


The present chapter deals with the intricacies of non-abelian gauge field theories. We consider the extension of local gauge transformations of QED, with the gauge group U(1) of phase transformations, to SU(N) groups.


  1. 1.
    Abe, K. et al. (1999). Measurement of R = σ Lσ T for. 03 < x < 0. 1 and fit to world data. Physics Letters, B452, 194–200.Google Scholar
  2. 2.
    Aad, G. et al. (2012). Observation of a new particle in the search for the Standard Model Higgs Boson with the ATLAS detector at the LHC. Physics Letters, B716, 1–29.ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Airapetian, A. et al. (2002). Measurement of R = σ Lσ T in deep ineastic scattering. arXiv:hep-ex/0210068.Google Scholar
  4. 4.
    Ali, A. et al. (1980). A QCD analysis of the high energy e + e data from PETRA. Physics Letters, 93B, 155–160.ADSCrossRefGoogle Scholar
  5. 5.
    Altarelli, G., & Parisi, G. (1977). Asymptotic freedom in parton language. Nuclear Physics, B126, 298–318.ADSCrossRefGoogle Scholar
  6. 6.
    Altmann, M. et al. (2005). Complete results for five years of GNO solar neutrino observations. Physics Letters, B616, 174–190.ADSCrossRefGoogle Scholar
  7. 7.
    Ambrosio, M. et al. (1998). Measurement of the atmospheric neutrino induced upgoing muon flux using MACRO. Physics Letters, B434, 451–457.ADSCrossRefGoogle Scholar
  8. 8.
    Ammar, R. et al. (1998). Measurement of the total cross section for e+e →  Hadrons at \(\sqrt{s} = 10.52\) GeV. Physical Review, D57, 1350–1358.ADSGoogle Scholar
  9. 9.
    Andivahis, L. et al. (1994). Measurements of the electric and magnetic form factors of the proton from Q 2 = 1.75 to 8.83 (GeV/c)2. Physical Review, D50, 5491–5517.ADSGoogle Scholar
  10. 10.
    Anselmann, P. et al. (1992). Solar neutrinos observed by GALLEX at Gram Sasso. Physics Letters, B285, 376–389.ADSCrossRefGoogle Scholar
  11. 11.
    Appelquist, T., & Georgi, H. (1973). e+e annihilation in gauge theories of strong interactions. Physical Review, D8, 4000–4002.ADSGoogle Scholar
  12. 12.
    Athanassopoulos, C. et al. (1998). Results on ν μ → ν e neutrino oscillations from the LSND experiment. Physical Review Letters, 81, 1774–1777.ADSCrossRefGoogle Scholar
  13. 13.
    Baikov, P. A., Chetyrkin, K. G., & Khun, J. H. (2008). Order α s 4 QCD corrections to Z and τ decays. Physical Review Letters, 101, 012002.ADSCrossRefGoogle Scholar
  14. 14.
    Bartel, W. et al. (1980). Observations of planar three-jet events in e e + annihilation and evidence for gluon bremsstrahlung. Physics Letters, 91B, 142–147.ADSCrossRefGoogle Scholar
  15. 15.
    Becchi, C., Rouet, A., & Stora, R. (1975). Renormalization of the Abelian Higgs-Kibble model. Communications in Mathematical Physics, 42, 127–162.ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Berger, C. et al. (1979). Evidence for gluon bremsstrahlung in e + e annihilation at high energies. Physics Letters, 86B, 418–425.ADSCrossRefGoogle Scholar
  17. 17.
    Beringer, J. et al. (2012). Particle data group. Physical Review D, 86, 010001.ADSCrossRefGoogle Scholar
  18. 18.
    Bjorken, J. D. (1969). Asymptotic sum rules at infinite momentum. Physical Review, 179, 1547–1553.ADSCrossRefGoogle Scholar
  19. 19.
    Bjorken, J. D., & Bodsky, S. J. (1970). Statistical model for electron-positron annihilation into hadrons. Physical Review, D1, 1416–1420.ADSGoogle Scholar
  20. 20.
    Bjorken, J. D., & Drell, S. D. (1964). Relativistic quantum mechanics. New York/San Francisco/London: McGraw-Hill.zbMATHGoogle Scholar
  21. 21.
    Bjorken, J. D., & Drell, S. D. (1965). Relativistic quantum fields. New York/San Francisco/London: McGraw-Hill.zbMATHGoogle Scholar
  22. 22.
    Bjorken, J. D., & Pachos, E. A. (1969). Inelastic electron-proton and y-proton scattering and the structure of the nucleon. Physical Review, 185, 1975–1982.ADSCrossRefGoogle Scholar
  23. 23.
    Bloom, E. D. et al. (1969). High- Energy Inelastic e-p Scattering at 6 and 10. Physical Review Letters, 23, 93–934.ADSGoogle Scholar
  24. 24.
    Bodek, A. et al. (1979). Experimental studies of the neutron and proton electromagnetic structure functions. Physical Review, D20, 1471–1552.ADSGoogle Scholar
  25. 25.
    Brandelik, R. et al. (1979). Evidence for planar events in e + e annihilation at high energies. Physics Letters, 86B, 243–249.ADSCrossRefGoogle Scholar
  26. 26.
    Brown, L. S., & Weisberger, W. I. (1979). Remarks on the static potential in quantum chromodynamics. Physical Review, D20, 3239–3245.ADSGoogle Scholar
  27. 27.
    Cabibbo, N. (1963). Unitary symmetry and leptonic decays. Physical Review Letters, 10, 531–533.ADSCrossRefGoogle Scholar
  28. 28.
    Callan, C. G., & Gross, D. J. (1969). High-energy electroproduction and the constitution of the electric current. Physical Review Letters, 22, 156–159.ADSCrossRefGoogle Scholar
  29. 29.
    Caswell, W. E. (1974). Asymptotic behavior of Non-Abelian gauge theories to two-loop order. Physical Review Letters, 33, 244–246.ADSCrossRefGoogle Scholar
  30. 30.
    Chatrchyan, S. et al. (2012). Observation of a new boson at mass 125 GeV with the CMS Experiment at LHC. Physics Letters, B716, 30–61.ADSCrossRefGoogle Scholar
  31. 31.
    Cleveland, B. T. et al. (1998). Measurement of the solar electron neutrino flux with the homestake chlorine detector. Astrophysics Journal, 496, 505–526.ADSCrossRefGoogle Scholar
  32. 32.
    Creutz, M. (1983). Quarks, gluons and lattices. Cambridge: Cambridge University Press.Google Scholar
  33. 33.
    Danby, G. et al. (1962). Observation of high-energy neutrino reactions and the existence of two kinds of neutrinos. Physical Review Letters, 9, 36–44.ADSCrossRefGoogle Scholar
  34. 34.
    Davis, R. et al. (1968). Search for neutrinos from the sun. Physical Review Letters, 20, 1205–1209.ADSCrossRefGoogle Scholar
  35. 35.
    Eidelman, S. et al. (2004). Particle data group. Physics Letters, B592, 1.ADSCrossRefGoogle Scholar
  36. 36.
    Erler, J. (1999). Calculation of the QED coupling \(\hat{\alpha }(M_{Z})\) in the modified minimal subtraction scheme. Physical Review D, 59, 054008, 1–7.Google Scholar
  37. 37.
    Faddeev, L. D., & Popov, V. N. (1967). Feynman diagrams for the Yang-Mills field. Physics Letters, B25, 29–30.ADSCrossRefGoogle Scholar
  38. 38.
    Fermi, E. (1934a). Tentativo di una teoria dei raggi β. Nuovo Cimento, 11, 1–19.zbMATHCrossRefGoogle Scholar
  39. 39.
    Fermi, E. (1934b). Versuch einer Theorie der β - Strahlen. Zeitschrift fur Physik, 88, 161–171.ADSzbMATHCrossRefGoogle Scholar
  40. 40.
    Feynman, R. P. (1963). Quantum theory of gravitation. Acta Physica Polonica, 24, 697–722.MathSciNetGoogle Scholar
  41. 41.
    Feynman, R. P. (1969a). The behavior of hadron collisions at extreme energies. In Proceedings of the 3rd Topical Conference on High Energy Collisions, Stony Brook. New York: Gordon & Breach.Google Scholar
  42. 42.
    Feynman, R. P. (1969b). Very high-energy collisions of hadrons. Physical Review Letters, 23, 1415–1417.ADSCrossRefGoogle Scholar
  43. 43.
    Feynman, R. P., & Gell-Mann, M. (1958). Theory of fermi interaction. Physical Review, 109, 193–198.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Field, R. D. (1989). Applications of perturbative QCD. Redwood City: Addison-Welry.Google Scholar
  45. 45.
    Field, R. D., & Feynman, R. P. (1977). Quark elastic scattering as a source of high-transverse-momentum mesons. Physical Review, D15, 2590–2616.ADSGoogle Scholar
  46. 46.
    Field, R. D., & Feynman, R. P. (1978). A parametrization of the properties of quark jets. Nuclear Physics, B136, 1–76.ADSCrossRefGoogle Scholar
  47. 47.
    Friedman, J. I., & Kendall, H. W. (1972). Deep inelastic electron scattering. Annual Review of Nuclear and Particle Science, 22, 203–254.ADSCrossRefGoogle Scholar
  48. 48.
    Fritzsch, H., & Gell-Mann, M. (1972). Quatks and what else? In J. D. Jackson & A. Roberts (Eds.), Proceedings of the XVI International Conference on High Energy Physics (Vol. 2). Chicago: Chicago University Press.Google Scholar
  49. 49.
    Fritzsch, H., Gell-Mann, M., & Leutwyler, H. (1973). Advantages of the color octet gluon. Physics Letters, B47, 365–368.ADSCrossRefGoogle Scholar
  50. 50.
    Fukuda, Y. et al. (1998). Evidence for oscillations of atmospheric neutrinos. Physical Review Letters, 81, 1562–1567.ADSCrossRefGoogle Scholar
  51. 51.
    Fukuda, Y. et al. (2002). Determination of solar neutrino oscillation parameters using 1496 days of Super-Kamiokande-I data. Physics Letters, B539, 179–187.ADSCrossRefGoogle Scholar
  52. 52.
    Gell-Mann, M. (1964). A schematic model of baryons and mesons. Physics Letters, 8, 214–215.ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Gell-Mann, M. (1972). Quarks. Acta Physica Austriaca Supplement IX, 9, 733–761.Google Scholar
  54. 54.
    Gell-Mann, M., Raymond, P., & Slansky, R. (1979). Complex spinors and unified theories. In P. van Nieuwenhuizen & D. Z. Friedman (Eds.), Supergravity. Amsterdam: North-Holland.Google Scholar
  55. 55.
    Glashow, S. L. (1961). Partial symmetries of weak interactions. Nuclear Physics, 22, 579–588.ADSCrossRefGoogle Scholar
  56. 56.
    Glashow, S. L., Iliopoulos, J., & Maiani, L. (1970). Weak interactions with Lepton-Hadron symmetry. Physical Review, D2, 1285–1292.ADSGoogle Scholar
  57. 57.
    Goldhaber, M., Grodzins, L., & Sunyar, A. W. (1958). Helicity of the neutrinos. Physical Review, 109, 1015–1017.ADSCrossRefGoogle Scholar
  58. 58.
    Greenberg, O. W. (1964). Spin and unitary spin independence in a paraquark model of baryons and mesons. Physical Review Letters, 13, 598–602.ADSCrossRefGoogle Scholar
  59. 59.
    Gribov, V. N., & Pontecorvo, B. (1969). Neutrino astronomy and lepton charge. Physics Letters, B616, 174–190.Google Scholar
  60. 60.
    Guth, A. H. (1980). Existence proof of a nonconfining phase in four-dimensional U(1) lattice theory. Physical Review, D21, 2291–2307.ADSMathSciNetGoogle Scholar
  61. 61.
    Halzen, F., & Martin, A. D. (1984). Quarks and leptons: An introductory course in modern particle physics. New York: Wiley.Google Scholar
  62. 62.
    Hampel, W. et al. (1999). GALLEX solar neutrino observations: Results for GALLEX IV. Physics Letters, B447, 127–133.ADSCrossRefGoogle Scholar
  63. 63.
    Han, M. Y., & Nambu, Y. (1965). Three-triplet model with double SU(3) symmetry. Physical Review, 139, B1006–B1010.ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    Hanson, G. et al. (1975). Evidence for jet structures in hadron production by e+e annihilation. Physical Review Letters, 35, 1609–1612.ADSCrossRefGoogle Scholar
  65. 65.
    Hirata, K. S. et al. (1996). Solar neutrino data covering solar cycle 22. Physical Review Letters, 77, 1683–1686.ADSCrossRefGoogle Scholar
  66. 66.
    Hoyer, P. et al. (1979). Quantum chromodynamics and jets in e + e . Nuclear Physics, B161, 349–372.ADSCrossRefGoogle Scholar
  67. 67.
    Itzykson, C., & Zuber, J.-B. (1980). Quantum field theory. New York/Toronto: McGraw-Hill.zbMATHGoogle Scholar
  68. 68.
    Joglekar, S. D., & Lee, B. W. (1976). General theory of renormalization of gauge invariant operators. Annals of Physics, 97, 160–215.ADSMathSciNetCrossRefGoogle Scholar
  69. 69.
    Jones, D. R. T. (1974). Two-loop diagrams in Yang-Mills theory. Nuclear Physics, B75, 531–538.ADSCrossRefGoogle Scholar
  70. 70.
    Jost, R., & Luttinger, J. M. (1950). Vacuum polarization and e4 charge renormalization for electrons. Helvetica Physica Acta, 23, 201.MathSciNetGoogle Scholar
  71. 71.
    Kobayashi, M., & Maskawa, K. (1973). CP violation in the renormalizable theory of weak interaction. Progress of Theoretical Physics, 49, 652–657.ADSCrossRefGoogle Scholar
  72. 72.
    Kogut, J. B. (1980). Progress in lattice theory. Physics Reports, 67, 67–102.ADSMathSciNetCrossRefGoogle Scholar
  73. 73.
    Kogut, J. B., Pearson, R. P., & Shigemitsu, J. (1981). The string tension, confinement and roughening in SU(3) Hamiltonian lattice gauge theory. Physics Letters, 98B, 63–68.ADSMathSciNetCrossRefGoogle Scholar
  74. 74.
    Landau, L. D. (1957). On the Conservation Laws for Weak Interactions. Nuclear Physics, 3, 127–131.ADSMathSciNetCrossRefGoogle Scholar
  75. 75.
    Langacker, P. (1981). Grand unified theories and proton decay. Physics Reports, 72, 185–385.ADSCrossRefGoogle Scholar
  76. 76.
    Lautrup, B., & Nauenberg, M. (1980). Phase transition in four-dimensional compact QED. Physics Letters, 95B, 63–66.ADSCrossRefGoogle Scholar
  77. 77.
    Lee, B. (1976). In R. Balian & J. Zinn-Justin (Eds.), Methods in field theory. Amsterdam: North Holland.Google Scholar
  78. 78.
    Lee, T. D., & Yang, C. N. (1956). Question of parity conservation in weak interactions. Physical Review, 104, 254–258. See also ibid., 106, 1671 (1957).Google Scholar
  79. 79.
    Lepage, G. P., & Brodsky, S. J. (1979). Exclusive processes in quantum chromodynamics: The form factors of baryons at large momentum transfer. Physical Review Letters, 43, 545–549.ADSCrossRefGoogle Scholar
  80. 80.
    Lepage, G. P., & Brodsky, S. J. (1980). Exclusive processes in perturbative quantum chromodynamics. Physical Review, D22, 2157–2198.ADSGoogle Scholar
  81. 81.
    Maki, Z., Nakagawa, M., & Sakata, S. (1962). Remarks on the unified model of elementary particles. Progress of Theoretical Physics, 28, 870–880.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  82. 82.
    Manoukian, E. B. (1984a). Proof of the decoupling theorem of field theory in Minkowski space. Journal of Mathematics and Physics, 25, 1519–1523.MathSciNetCrossRefGoogle Scholar
  83. 83.
    Manoukian, E. B. (1985). Quantum action principle and path integrals for long-range interactions. Nuovo Cimento, 90A, 295–307.ADSCrossRefGoogle Scholar
  84. 84.
    Manoukian, E. B. (1986a). Action principle and quantization of gauge fields. Physical Review, D34, 3739–3749.ADSMathSciNetGoogle Scholar
  85. 85.
    Manoukian, E. B. (1986b). Generalized conditions for the decoupling theorem of quantum field theory in Minkowski space with particles of vanishing small masses. Journal of Mathematics and Physics, 27, 1879–1882.MathSciNetCrossRefGoogle Scholar
  86. 86.
    Manoukian, E. B. (1987). Functional differential equations for gauge theories. Physical Review, D35, 2047–2048.ADSMathSciNetGoogle Scholar
  87. 87.
    Manoukian, E. B. (2006). Quantum theory: A wide spectrum. Dordrecht: Springer.zbMATHGoogle Scholar
  88. 88.
    Martin, P. C., & Glashow, S. L. (2008). Julian Schwinger 1918-1994: A biographical memoir. National Academy of Sciences, Washington, DC, Copyright 2008.Google Scholar
  89. 89.
    Mele, S. (2006). Measurements of the running of the electromagnetic coupling at LEP. In XXVI Physics in Collision, 6–9 July 2006, Búzios, Rio de Janeiro.Google Scholar
  90. 90.
    Minkowski, P. (1977). μ → ey at a rate of one out of 109 muon decays? Physics Letters, B67, 421–428.ADSCrossRefGoogle Scholar
  91. 91.
    Miura, M. (2010). Search for nucleon decays in Super-Kamiokande. ICHEP, Paris, Session, 10, 408–412.Google Scholar
  92. 92.
    Mohapatra, R. N., & Senjanović, G. (1980). Neutrino mass and spontaneous parity nonconservation. Physical Review Letters, 44, 912–915.ADSCrossRefGoogle Scholar
  93. 93.
    Mohr, P. J. et al. (2008). CODATA recommended values of the fundamental physical constants. Reviews of Modern Physics, 80, 633–730.ADSCrossRefGoogle Scholar
  94. 94.
    Olive, K. A. et al. (2014). Particle data group. Chinese Physics C, 38, 090001.ADSCrossRefGoogle Scholar
  95. 95.
    Panofski, W. (1968). In Proceedings of the 14th International Conference on High Energy Physics (pp. 23–39). CERN Scientific Information, Vienna.Google Scholar
  96. 96.
    Pauli, W. (1957). On the earlier and more recent history of the neutrino. In: Winter, K. (Ed.), Neutrino physics. Cambridge: Cambridge University Press (1991).Google Scholar
  97. 97.
    Perrin, F. (1933). Possibilité d’Emission de Particules Neutres de Masse Nulle dans les Radioactivités β. Comptes Rendus Academie des Sciences Paris, 197, 1625.zbMATHGoogle Scholar
  98. 98.
    Peskin, M. (1997). Beyond the Standard Model. In N. Ellis & M. Neubert (Eds.), European School of High-Energy Physics 1996, CERN-97-03, Genève.Google Scholar
  99. 99.
    Pontecorvo, B. (1957). Mesonium and Anti-Mesonium. Soviet Physics JETP, 33, 549–551. Original Russian Version: Zhurnal Experimental’noi i Teoreticheskoi Fiziki, 6, 429–431 (1957).Google Scholar
  100. 100.
    Pontecorvo, B. (1958). Inverse beta processes and nonconservation of lepton charge. Soviet Physics JETP, 34, 247–248. Original Russian Version: Zhurnal Experimental’noi i Teoreticheskoi Fiziki, 7, 172–173 (1957).Google Scholar
  101. 101.
    Pontecorvo, B. (1968). Neutrino experiments and the problem of conservation of Leptonic charge. Soviet Physics JETP, 53, 1717–1725. Original Russian Version: Zhurnal Experimental’noi i Teoreticheskoi Fiziki, 26, 984–988 (1967).Google Scholar
  102. 102.
    Puckett, A. J. R. et al. (2012). Final analysis of proton form factor ratio at Q 2 = 4. 0, 4.8 and 5.6 GeV2. Physical Review, C85, 045203.Google Scholar
  103. 103.
    Punjabi, V. et al. (2005). Proton elastic From factor ratios to Q 2 = 3, 5 GeV2 by polarization transfer. Physical Review, C71, 055202.ADSGoogle Scholar
  104. 104.
    Reines, F., & Cowan, C. L. (1956). The neutrino. Nature, 178, 446–449.ADSCrossRefGoogle Scholar
  105. 105.
    Riordan, E. M. et al. (1974). Extraction of R = σ Lσ T from deep inelastic e​ −​ p and e​ −​ d cross sections. Physical Review Letters, 33, 561–564.ADSCrossRefGoogle Scholar
  106. 106.
    Salam, A. (1957). Parity consevation and a two-component theory of the neutrino. Nuovo Cimento, 5, 299–301.MathSciNetCrossRefGoogle Scholar
  107. 107.
    Salam, A. (1968). Weak and electromagnetic interactions. In N. Svartholm (Ed.), Elementary Particle Theory, Proceedings of the 8th Nobel Symposium, Almqvist and Wiksell, Stockholm.Google Scholar
  108. 108.
    Salam, A., & Ward, J. (1964). Electromagnetic and weak interactions. Physics Letters, 13, 168–170.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    Schwinger, J. (1957). A theory of the fundamental interactions. Annals of Physics, 2, 407–434.ADSMathSciNetzbMATHCrossRefGoogle Scholar
  110. 110.
    Slavnov, A. A. (1972). Ward identities in gauge theories. Theoretical and Mathematical Physics, 10, 152–160. English Translation: Theoretical and Mathematical Physics, 10, 99–108 (1972).Google Scholar
  111. 111.
    Sterman, G., & Weinberg, S. (1977). Jets from quantum chromodynamics. Physical Review Letters, 39, 1436–1439.ADSCrossRefGoogle Scholar
  112. 112.
    Stevenson, P. M. (1978). Comments on the Sterman-Weinberg jet formula. Physics Letters, 78B, 451–454.ADSCrossRefGoogle Scholar
  113. 113.
    Sudarshan, E. C. G., & Marshak, R. (1958). Chirality invariance and the universal fermi interaction. Physical Review, 109, 1860–1862.ADSCrossRefGoogle Scholar
  114. 114.
    ’t Hooft, G. (1971a). Renormalizable of massless Yang-Mills fields. Nuclear Physics, B33, 173–199.Google Scholar
  115. 115.
    ’t Hooft, G. (1971b). Renormalizable Lagrangians for massive Yang-Mills fields. Nuclear Physics, B35, 167–188.Google Scholar
  116. 116.
    ’t Hooft, G. (1971c). Prediction for neutrino-electron scattering cross sections in weinberg’s model of electroweak interaction. Physics Letters, B37, 195–196.Google Scholar
  117. 117.
    Taylor, J. C. (1971). Ward identities and charge renormalization. Nuclear Physics, B33, 436–444.ADSCrossRefGoogle Scholar
  118. 118.
    Veltman, M. J. G. (1981). The infrared-ultraviolet connection. Acta Physica Polonica, B12, 437.Google Scholar
  119. 119.
    Vilain, P. et al. (1994). Precision Measurement of Electroweak Parameters from the Scattering of Muon-Neutrinos on Electrons. Physics Letters B, 335, 246–252.ADSCrossRefGoogle Scholar
  120. 120.
    Weinberg, S. (1967). A Model of Leptons. Physical Review Letters, 19, 1264–1266.ADSCrossRefGoogle Scholar
  121. 121.
    Weinberg, S. (1996). The Quantum Theory of Fields, II: Modern Applications. Cambridge University Press, Cambridge.zbMATHCrossRefGoogle Scholar
  122. 122.
    Wu, C. S. et al. (1957). Experimental tests of parity conservation in beta decay. Physical Review, 105, 1413–1415.ADSCrossRefGoogle Scholar
  123. 123.
    Yanagida, Y. (1980). Horizontal symmetry and masses of neutrinos. Progress of Theoretical Physics, 64, 1103–1105.ADSCrossRefGoogle Scholar
  124. 124.
    Zee, A. (1973). Electron-positron annihilation in stagnant field theories. Physical Review, D8, 4038–4041.ADSGoogle Scholar
  125. 125.
    Zweig, G. (1964). An SU3 Model for strong interaction symmetry and its breaking. CERN Preprint, TH-401, 1–24.Google Scholar

Recommended Reading

  1. 1.
    Beringer, J. et al. (2012). Particle data group. Physical Review D, 86, 010001.ADSCrossRefGoogle Scholar
  2. 2.
    DeWitt, B. (2014). The global approach to quantum field theory. Oxford: Oxford University Press.zbMATHGoogle Scholar
  3. 3.
    Manoukian, E. B. (1981). Generalized decoupling theorem in quantum field theory. Journal of Mathematics and Physics, 22, 2258–2262.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Manoukian, E. B. (1984). Proof of the decoupling theorem in Minkowski space. Journal of Mathematics and Physics, 25, 1519–1523.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Manoukian, E. B. (1986a). Generalized conditions for the decoupling theorem of quantum field theory in Minkowski space with particles of vanishingly small masses. Journal of Mathematics and Physics, 27, 1879–1882.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Manoukian, E. B. (1986b). Action principle and quantization of gauge fields. Physical Review, D34, 3739–3749.ADSMathSciNetGoogle Scholar
  7. 7.
    Manoukian, E. B. (1987). Functional differential equations for gauge theories. Physical Review, D35, 2047–2048.ADSMathSciNetGoogle Scholar
  8. 8.
    Olive, K. A. et al. (2014). Particle Data Group. Chinese Physics C, 38, 090001.ADSCrossRefGoogle Scholar
  9. 9.
    Ross, G. G. (1985). Grand Unified Theories. Reading: Benjamin/Cummings Publishing.Google Scholar
  10. 10.
    Weinberg. S. (1996). The Quantum Theory of Fields. II: Modern Applications. Cambridge: Cambridge University Press.zbMATHCrossRefGoogle Scholar
  11. 11.
    Yongram, N., Manoukian, E. B., & Siranan, S. (2006). Polarization correlations in muon pair production in the electroweak model. Modern Physics Letters A, 21, 979–984.ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Edouard B. Manoukian
    • 1
  1. 1.The Institute for Fundamental StudyNaresuan UniversityPhitsanulokThailand

Personalised recommendations