# Interaction terms

1. Apr 5, 2008

### robousy

Hey folks,

I have a pretty interesting Lagrangian setup:

$$\mathcal{L}=-\frac{1}{4}(\nabla_a u_b -\nabla_b u_a)(\nabla^a u^b -\nabla^b u^a)-\lambda(u_au^a-v^2)-\frac{1}{2}(\partial\phi^2)-\frac{1}{2}m^2\phi^2-\frac{1}{2\mu^2}u^au^b\partial_a\phi\partial_b\phi$$

My term $u^a$ is a spacelike 5 vector that violates Lorentz Invariance in the 5th dimension only. The indices a,b run from 0 to 4.

My question:

In the paper I'm reading (http://arxiv.org/PS_cache/arxiv/pdf/...802.0521v1.pdf [Broken]), the above lagrangian is referred to have "the lowest order coupling". I'm guessing this comes from the last interaction term between $u$ and $\phi$. Can anyone explain why the term has to be of the form $$\frac{1}{2\mu^2}u^au^b\partial_a\phi\partial_b\phi$$. Whats wrong with just $$\frac{1}{2\mu^2}u^au_a\phi^2$$ for example??

Last edited by a moderator: May 3, 2017
2. Apr 5, 2008

### humanino

Hi,

can you please provide the complete link to the paper ?
Thanks !

3. Apr 5, 2008