Question

How to get “massless” equation of motion from the action of Nordstrom scalar field theory?

Answer 1

There is Nordstrom theory of the particle moving in a scalar field φ(x)φ(x):

S=−m∫eφ(x)ηαβdxαdλdxβdλ−−−−−−−−−−√dλ.S=−m∫eφ(x)ηαβdxαdλdxβdλdλ.

How to get the equation of motion for massless objects? In this case I may introduce new parameter ηαβdxαdλdxβdλ−−−−−−−−√dλ=dτmηαβdxαdλdxβdλdλ=dτm.

But when I try to derive (like this way) the equations of motion, I get

∂αφ=m2ddτ(uαeφ)e−φ.∂αφ=m2ddτ(uαeφ)e−φ.

Unfortunately, this equation doesn't predict the absense of deflection of light. But Nordstrom theory really predicts the deflection of light. So where is the mistake in my reasoning?

Addition.

I got the mistake. By introducing new parameter ττ I must rewrite my equation in a form

∂αφ=1m2ddτ(pαeφ)e−φ.∂αφ=1m2ddτ(pαeφ)e−φ.

So it really preficts no deflection of light.

Answer 2

Hey mate ^_^

You can get “massless” equation of motion from the action of Nordstrom scalar field theory. Check this attachment.

#Be Brainly♥️