Find the spectrum of the 2nd excited states.

[rbwang1225]

Homework Statement

A state at the 2nd exited level is of the form:
$|\epsilon>=(\epsilon_{\mu\nu}\alpha^\mu_{-1}\alpha^\nu_{-1}+\epsilon_{\mu}\alpha^\nu_{-2})|0;p>$
Find the spectrum of the 2nd excited states, the value of the mass squared, the condition for the state to be physical, and the gauge symmetry transformation due to null states.

Homework Equations

I don't know much.

The Attempt at a Solution

Any advice would be appreciated!

 

[mark726]

I would suggest starting by breaking down the given state into its components and understanding what each term represents. The notation may seem intimidating, but it is important to understand the physical meaning behind it.

Next, I would suggest using the appropriate equations and principles from your knowledge of quantum mechanics and particle physics to derive the spectrum of the 2nd excited states and the value of the mass squared. This may involve manipulating the operators and using commutation relations.

To determine the condition for the state to be physical, you may need to consider the constraints on the state imposed by the theory. This could involve looking at the gauge symmetry and any conservation laws that apply.

Finally, to understand the gauge symmetry transformation due to null states, you may need to investigate the concept of null states and how they affect the physical states in the theory. This could involve looking at the generators of the gauge symmetry and how they act on the state.

Overall, my advice would be to approach this problem systematically, breaking it down into smaller parts and using your knowledge and understanding of the relevant principles and equations to solve each part. Don't be afraid to consult textbooks or other resources for guidance. Good luck!