Saturday, 24 September 2016

hilbert space - What happens to the global $U(1)$ symmetry in alternative formulations of Quantum Mechanics?


The global $U(1)$ symmetry in Quantum Mechanics corresponds to the freedom to shift the phase of the wave function $$ \Psi \to e^{i\varphi} \Psi \, $$ and can be used to understand the conservation of electric charge.



Where, if at all, does this symmetry show up in alternative formulations of Quantum Mechanics, such as



  • the path integral formulation,

  • the phase space formulation,

  • the pilot wave formulation?




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