Symplectic Field Theories: Scalar and Spinor Representations - Costa, Caroline [UNESP]; Tenser, Marcia R.; Amorim, Ronni G. G.; Fernandes, Marco C. B.; Santana, Ademir E.; Vianna, J. David M. (Springer, 2018)
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.
Keywords: Moyal product; Phase space; Field theory