(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi

I was reviewing this paper.

But I stuck in the last part. (equation 25)

According to the paper the Lagrangian is -

[tex]2L=(\dot{V^{T})^{2}}-(\nabla\times V^{T})^{2}+[\dot{B}^{T}-\nabla\times A^{T}]^{2}+2mV^{T}.(\nabla\times A^{T})+2mB^{T}.\dot{V}^{T}+2\mu^{2}A^{T}.B^{T}------(1)[/tex]

And after imposing the conditions below-

[tex]B^{L}=A^{L}=0=\dot{V^{L}}-\nabla U------(2)[/tex]

[tex]A^{T}.B^{T}=-(\nabla\times A^{T}).(\nabla^{2})^{-1}(\nabla\times B^{T})------(3)[/tex]

[tex](\nabla\times A^{T})=\dot{B^{T}}-mV^{T}+\mu^{2}(\nabla^{2})^{-1}(\nabla\times B^{T})------(4)[/tex]

There would be only two terms (according to the paper)-

[tex]2L= (\dot{V^{T})^{2}}+\mathbf{V}^{T}\nabla^{2}\mathbf{V}^{T}[/tex]

My Calculation:

But after I use the condition (2), (3) and (4) and put them into (1). But I have found the equation-

[tex]2L= (\dot{V^{T})^{2}}+\mathbf{V}^{T}\nabla^{2}\mathbf{V}^{T}+2mB^{T}.\dot{V}^{T}-m^{2}(V^{T})^{2}-\mu^{4}(\nabla^{2})^{-2}(\nabla\times B^{T})^{2} [/tex]

[tex]+2\dot{B}^{T}mV^{T}+2mV^{T}\mu^{2}(\nabla^{2})^{-1}(\nabla\times B^{T})-2\mu^{2}(\nabla^{2})^{-1}(\nabla\times B^{T})\dot{B}^{T}[/tex]

So there are some extra terms that need to be eliminated.

How can I do it? Is there any other condition that needed to be applied? Please help.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Coupling of vector gauge to a tensor field problem

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**