I am trying to fully understand the spectrum structure in the paper "A LAGRANGIAN FORMULATION OF THE CLASSICAL AND QUANTUM DYNAMICS OF SPINNING PARTICLES " by Brink, Vecchia and Howe. (I attached the file)(adsbygoogle = window.adsbygoogle || []).push({});

I am having a problem with equation (4.13). It writes [itex]p \cdot b|\psi_{phys}\rangle=0[/itex] but was supposed to be [itex]p \cdot \psi |\psi_{phys}\rangle= p \cdot \frac{1}{2}(b + b^{\dagger})|\psi_{phys}\rangle=0[/itex] by constraint (4.3). Why is the [itex]b^{\dagger}[/itex] omitted from equation (4.13)? Am I missing something in understating how [itex]b^{\dagger}[/itex] acts on the spectrum? Am I missing something with the identification of [itex]b[/itex] and [itex]b^{\dagger}[/itex] as creation and destroying operators?

Thanks.

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# A Trying to understand constraint equation from paper by Brink

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