Non-Linear Abelian Scenarios and Yang-Mills Theory


  • Saulo Machado Moreira Sousa Brazilian Center for Physical Research
  • I. Soares Centro Brasileiro de Pesquisas Fsicas, Rio de Janeiro RJ, 22290-180, Brazil.
  • D. Leite Centro Brasileiro de Pesquisas Fsicas, Rio de Janeiro RJ, 22290-180, Brazil.
  • R. M. Doria Quarks, Petropolis, 25600, RJ, Brazil



We present a natural formulation for constructing Yang-Mills theories from the incorporation of non-linearities to the Maxwell's theory of electromagnetism. Our formulation is strongly based on Noether's Theorem and aims to show how the introduction of non-linearities can turn a global invariance into a local symmetry as the more general Yang-Mills type of symmetry.


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[1] C. N. Yang and R. L. Mills. Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev., 96:191{195, Oct 1954.
[2] R. Shaw. The Problem of Particle Types and Other Contributions to the Theory of Elementary Particles. PhD thesis, Cambridge, UK, 1955.
[3] C. N. Yang. Selected Papers (1945-1980) of Chen Ning Yang: With Commentary. World Scientic, 2005.
[4] G. Hooft. 50 Years of Yang-Mills Theory. World Scientic, 2005.
[5] S. Deser. The limit of massive electrodynamics. Annalesde l'I.H.P. Physique thorique, 16(1):79{85, 1972.
[6] S. Deser. Gravity from self-interaction in a curved background. Classical and Quantum Gravity, 4(4):L99, 1987.
[7] D G. Boulware, S Deser, and J H. Kay. Supergravity from self-interaction. 96:141{162, 04 1979.
[8] John David Jackson. Classical Electrodynamics. John Wiley & Sons, 1975.
[9] Renato Doria. A new model for a non-linear electromagnetic model with self-interacting photons. Journal of Advances in Physics, 7(3):1840{1896, 2011.
[10] H. C. Corben and Julian Schwinger. The electromagnetic properties of mesotrons. Phys. Rev., 58:953{968, Dec 1940.
[11] A. Komar and Abdus Salam. Renormalization problem for vector meson theories. Nuclear Physics, 21:624 { 630, 1960.
[12] T. D. Lee and C. N. Yang. Theory of charged vector mesons interacting with the electromagnetic eld. Phys. Rev., 128:885{898, Oct 1962.
[13] Abdus Salam. Renormalizable electrodynamics of vector mesons. Phys. Rev., 130:1287{1290, May 1963.
[14] K. H. Tzou. Il Nuovo Cimento, 33:286, 1964.
[15] Abdus Salam and Robert Delbourgo. Renormalizable electrodynamics of scalar and vector mesons. ii. Phys. Rev., 135:B1398{B1427, Sep 1964.
[16] Giorgio Velo and Daniel Zwanzinger. Noncausality and other defects of interaction lagrangians for particles with spin one and higher. Phys. Rev., 188:2218{2222, Dec 1969.
[17] Harmon Aronson. Spin-1 electrodynamics with an elec- tric quadrupole moment. Phys. Rev., 186:1434{1441, Oct 7 1969.
[18] Bert Schroer. Peculiarities of massive vector mesons and their zero mass limits. The European Physical Journal C, 75(8):365, Aug 2015.
[19] M. Kuroda, J. Maalampi, K.H. Schwarzer, and D. Schildknecht. Non-standard self-interactions of the weak vector bosons and their phenomenological implications. Nuclear Physics B, 284:271 { 298, 1987.
[20] I. Kuss and D. Schildknecht. Discovering non-abelian weak couplings and an anomalous magnetic dipole moment of the w at lep 2. Physics Letters B, 383(4):470 { 474, 1996.
[21] M. Bilenky, J.L. Kneur, F.M. Renard, and D. Schildknecht. Trilinear couplings among the electroweak vector bosons and their determination at lep2. Nuclear Physics B, 409(1):22 { 68, 1993.
[22] Abdus Salam. Weak and electromagnetic interactions. In Nils Svartholm, editor, Elementary particle theory, pages 367{377. Almquist & Wiksell, 1968.
[23] S. Kamefuchi, L. O'Raifeartaigh, and Abdus Salam. Change of variables and equivalence theorems in quan- tum eld theories. Nuclear Physics, 28(1):529 { 549, 1961.
[24] Steven Weinberg. A model of leptons. Phys. Rev. Lett., 19:1264{1266, Nov 1967.
[25] H. Georgi and S.L. Glashow. Unity of all elementary particle forces. Phys. Rev. Lett., 32(438), Feb 1974.
[26] Sheldon L. Glashow. Partial-symmetries of weak interactions. Nuclear Physics, 22(4):579 { 588, 1961.
[27] Peter W. Higgs. Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett., 13:508{509, Oct 1964.
[28] S. Machado Moreira. Efeitos Eletrodina^amicos N~ao- Lineares e Sistemas Qua^anticos Abertos. PhD thesis, Centro Brasileiro de Pesquisas Fsicas, BRA, 2017.
[29] J. Chauca, R. Doria, and I. Soares. Four bosons electro- magnetism. Journal of Advances in Physics, 10(1):2605, 2015.
[30] S. A. Dias. Professor global class notes. Accessed: 2016.




How to Cite

Sousa, S. M. M., Soares, I., Leite, D., & Doria, R. M. (2017). Non-Linear Abelian Scenarios and Yang-Mills Theory. JOURNAL OF ADVANCES IN PHYSICS, 13(10), 5146–5154.