Question

Would it be possible for the stress-energy tensor (TμνTμν) to couple to a spin-1 anti-symmetric rank-2 field (like the electromagnetic field strength tensorFμνFμν)? If so, what would be the Lagrangian?

Answer 1

Yes, it is possible for the stress-energy tensor to couple to the electromagnetic field strength tensor. The Lagrangian for this coupling is -1/4 FμνFμν + AμJμ, where Fμν is the electromagnetic field strength tensor and Aμ is the vector potential.

Step-by-step explanation:

Yes, it is possible for the stress-energy tensor (Tμν) to couple to a spin-1 anti-symmetric rank-2 field like the electromagnetic field strength tensor (Fμν). The Lagrangian for this coupling can be written as:

L = -1/4 Fμν Fμν + Aμ Jμ

Here Fμν is the electromagnetic field strength tensor and Aμ is the vector potential. Jμ represents the current density and is given by Jμ = Tμν Aν. This Lagrangian describes the interaction between the stress-energy tensor and the electromagnetic field.