Question: Spin particles in scalar gravitational field

[Wenzi]

The action of non-spinning particles in scalar gravity is

S=-\int{\sqrt{-g}(\frac{1}{8\pi}g^{\mu\nu}\Phi_{,\mu}\Phi_{,\nu}-\rho e^{\Phi})d^4x}

where \rho presents the comoving density.
Now, I want to know the formula when particles with classical spin.

Thank you!

 

[Wenzi]

??

 

[Wenzi]

Anyone who can help me?

 

[Jonathan Scott]

Anyone who can help me?

I guess that may be too advanced or unusual a request for the frequent visitors such as myself; sooner or later you may get a useful reply, but in the mean time I suggest you try searching in Google and in the scientific literature. (I remember that in GR, a spinning particle is described by the Papapetrou equation, but that's probably not relevant here).

 

[Wenzi]

I guess that may be too advanced or unusual a request for the frequent visitors such as myself; sooner or later you may get a useful reply, but in the mean time I suggest you try searching in Google and in the scientific literature. (I remember that in GR, a spinning particle is described by the Papapetrou equation, but that's probably not relevant here).

haha, thank you!

I am waiting...

 

[Wenzi]

I guess that may be too advanced or unusual a request for the frequent visitors such as myself; sooner or later you may get a useful reply, but in the mean time I suggest you try searching in Google and in the scientific literature. (I remember that in GR, a spinning particle is described by the Papapetrou equation, but that's probably not relevant here).

Or, the question is equal to Stress-energy tensor of the spinning particles.

 

[tim_lou]

I don't know much about spin in GR but your question seems a bit vague. What formula do you want to know? the Einstein's equation for this action? Further, is the S the matter part? I assume so since the Ricci scalar part is missing.

Also, by classical spin, what do you mean? like fermions or what?

Perhaps others may be able to help after these clarifications.