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Classical Yang-Mills-Dirac equations: Qualitative analysis of some solutions with a noncompact symmetry group

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Abstract

We consider classical Yang-Mills and Yang-Mills-Dirac equations on Minkowski space, with gauge group SU(2), and look for solutions invariant (up to a gauge transformation) under SO(3)×SO0(1, 1) and SO0(2, 1)×SO(2), respectively. In each case, we analyze the qualitative features of the solutions, in particular the asymptotic behavior as the solution approaches its singularities. The method is based on standard theorems from the theory of nonlinear ordinary differential equations.

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References

  1. AntoineJ.-P., DąbrowskiL. and MaharaI.: Classical Yang-Mills-Dirac system with conformal symmetry: a geometrical analysis, Modern Phys. Lett. A 9 (1994), 3431–3444.

    Google Scholar 

  2. AntoineJ.-P. and JacquesM.: Classical Yang-Mills fields on Minkowski space with a non-compact invariance group, Classical Quantum Gravity 1 (1984), 431–446.

    Google Scholar 

  3. AntoineJ.-P., and JacquesM.: Classical Yang-Mills fields on Minkowski space with a non-compact symmetry and an arbitrary compact gauge group, Classical Quantum Gravity 4 (1987), 181–194.

    Google Scholar 

  4. AntoineJ.-P., LambertD. and SepulchreJ.-A.: Classical Yang-Mills fields with conformal invariance: from exact solutions to qualitative analysis, Classical Quantum Gravity 6 (1989), 295–310.

    Google Scholar 

  5. HarnadJ., ShniderS. and VinetL.: Group actions on principal bundles and invariance conditions for gauge fields, J. Math. Phys. 21 (1980), 2719–2724.

    Google Scholar 

  6. DoneuxJ., Saint-AubinY. and VinetL.: Matter-coupled Yang-Mills system in Minkowski space. II. Invariant solutions in the presence of Dirac spinor fields, Phys. Rev. D. 25 (1982), 484–501.

    Google Scholar 

  7. ArnoldV. I.: Ordinary Differential Equations, MIT Press, Cambridge, MA, 1978.

    Google Scholar 

  8. WigginsS.: Global Bifurcations and Chaos, Springer-Verlag, Berlin, 1988.

    Google Scholar 

  9. SanchezD.: Ordinary Differential Equations and Stability Theory: An Introduction, Freeman, San Francisco, 1962.

    Google Scholar 

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Authors and Affiliations

  1. Institut de Physique Théorique, Université Catholique de Louvain, B-1348, Louvain-la-Neuve, Belgium

    J. -P. Antoine & I. Mahara

  2. CTSPS, Clark Atlanta University, 30314, Atlanta, GA, USA

    I. Mahara

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  1. J. -P. Antoine
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  2. I. Mahara
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Antoine, J.P., Mahara, I. Classical Yang-Mills-Dirac equations: Qualitative analysis of some solutions with a noncompact symmetry group. Lett Math Phys 38, 237–255 (1996). https://doi.org/10.1007/BF00398349

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  • DOI: https://doi.org/10.1007/BF00398349

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