Symplectic Field Theories: Scalar and Spinor Representations
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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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Advances In Applied Clifford Algebras. Basel: Springer Basel Ag, v. 28, n. 1, 18 p., 2018.
