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Classical solutions of Yang-Mills theory (2020)

  • Authors:
  • USP affiliated author: FIUSA, GUILHERME CAMARGO - IFSC
  • School: IFSC
  • Language: Inglês
  • Abstract: In this work, we investigate the SU (2) Yang-Mills theory and derive two classes of classical solutions of physical interest, namely, monopoles and instantons. The monopole solutions arise when we consider the Higgs mechanism, by topological arguments and the homotopy group formalism, we conclude that the original symmetry group SU (2) is spontaneously broken down to U(1), in the process, the mass of gauge particles is generated and the connection between topological charge and magnetic charge is established for the monopole. We calculate the magnetic charge and the mass of the ‘t Hooft-Polyakov monopole. Then, we explore the Bogomolny bound and the Bogomolny-Prasad-Sommerfield monopole, wich is an exact solution. We briefly discuss of the Montonen-Olive duality. For instanton solutions, we consider a pure SU (2) Yang-Mills theory on a Euclidean space-time, we show that the self-duality condition minimizes the Euclidean action, hence, we construct self-dual instanton and N-instanton solutions and calculate their action, obtaining that the action of N-instantons is n times the action of a single instanton.
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    • ABNT

      FIUSA, Guilherme Camargo; FERREIRA, Luiz Agostinho. Classical solutions of Yang-Mills theory. [S.l: s.n.], 2020.
    • APA

      Fiusa, G. C., & Ferreira, L. A. (2020). Classical solutions of Yang-Mills theory. São Carlos.
    • NLM

      Fiusa GC, Ferreira LA. Classical solutions of Yang-Mills theory. 2020 ;
    • Vancouver

      Fiusa GC, Ferreira LA. Classical solutions of Yang-Mills theory. 2020 ;

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