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<p>In this work we study unitary symplectic representations of space-time symmetries associated with the Husimi function method. For the non-relativistic (Galilei) symmetry, a symplectic Schrödinger equation is derived. As application, cubic and quartic oscillators are addressed perturbatively. First-order corrected eigen functions for the ground and first excited states are obtained. Then the corresponding Husimi functions are computed. In the same context, the symplectic Klein-Gordon and Dirac equations are derived closely associated with a relativistic Husimi distribution. In this case, gauge symmetry is studied. As a basic result, gauge fields are accommodated within the context of the Husimi method. Specifically, the <i>U</i>(1)- gauge symmetry is preliminarly analyzed. </p>

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Symplectic Quantum Physics in Husimi Representation

  • 期刊论文

  • 发表日期：

    2025年12月6日

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  • G. X. A. Petronilo,
  • R. R. Luz,
  • A. E. Santana,
  • R. A. S. Paiva,
  • R. G. G. Amorim

摘要

In this work we study unitary symplectic representations of space-time symmetries associated with the Husimi function method. For the non-relativistic (Galilei) symmetry, a symplectic Schrödinger equation is derived. As application, cubic and quartic oscillators are addressed perturbatively. First-order corrected eigen functions for the ground and first excited states are obtained. Then the corresponding Husimi functions are computed. In the same context, the symplectic Klein-Gordon and Dirac equations are derived closely associated with a relativistic Husimi distribution. In this case, gauge symmetry is studied. As a basic result, gauge fields are accommodated within the context of the Husimi method. Specifically, the U(1)- gauge symmetry is preliminarly analyzed.