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Symplectic Field Theories: Scalar and Spinor Representations

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Abstract

Using elements of symmetry, as gauge invariance, aspects of field theories represented in symplectic space are introduced and analyzed under physical bases. The states of a system are described by symplectic wave functions, which are associated with the Wigner function. Such wave functions are vectors in a Hilbert space introduced from the cotangent-bundle of the Minkowski space. The symplectic Klein–Gordon and the Dirac equations are derived, and a minimum coupling is considered in order to analyze the Landau problem in phase space.

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Acknowledgements

This work was partially supported by CNPq of Brazil.

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Authors and Affiliations

  1. International Center of Physics, Instituto de Física, Universidade de Brasília, Brasília, DF, 70910-900, Brazil

    Caroline Costa, Marcia R. Tenser, Ronni G. G. Amorim, Marco C. B. Fernandes, Ademir E. Santana & J. David M. Vianna

  2. Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, SP, 01140-070, Brazil

    Caroline Costa

  3. Faculdade Gama, Universidade de Brasília, Brasília, DF, 72444-240, Brazil

    Ronni G. G. Amorim

  4. Instituto de Física, Universidade Federal da Bahia, Salvador, BA, 40210-340, Brazil

    J. David M. Vianna

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  1. Caroline Costa
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Correspondence to Ademir E. Santana.

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Costa, C., Tenser, M.R., Amorim, R.G.G. et al. Symplectic Field Theories: Scalar and Spinor Representations. Adv. Appl. Clifford Algebras 28, 27 (2018). https://doi.org/10.1007/s00006-018-0840-4

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