# A Trying to understand constraint equation from paper by Brink

1. Oct 7, 2017

### chenkr3

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

Thanks.

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2. Oct 13, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.