Recent content by jdstokes

I think the error lies in the fact that I should be considering the transformation of {\omega^a}_{b} rather than \omega_{ab}. The transformation rule for {\omega^a}_{b} is {\omega^a}_{b\mu}(x) \mapsto {\Lambda^\beta}_b(x) {\omega^\alpha}_{\beta\mu}(x) {\Lambda_{\alpha}}^a(x) + [\partial_\mu...

The action for a fermion in curved spacetime is S = -\int d^4 x \sqrt{- \det(\eta^{ab} e_{a\mu}e_{b\nu})} \left[ i\overline{\psi} e^\mu_a \gamma^a D_\mu \psi + i m \overline{\psi}\psi \right] where g_{\mu\nu} = \eta^{ab} e_{a\mu} e_{b\nu} and the derivative operator acting on fermions is...

I don't think the paper is correct. It is impossible to have ``diffeomorphism invariant physics with preferred frame effects''. The physics discussed in the paper is trivially coordinate invariant as I discussed above.

Any physical theory is Lorentz invariant. Heck, you can write the non-relativistic heat equation in Lorentz-invariant form if you want. The problem is that you can't write such theories in diffeomorphism-invariant form; i.e., without introducing background geometrical data. So to answer your...

Hi nrqed, Firstly, I'm very surprised to hear of the plethora of definitions out there for coordinate invariance/diffeomorphism invariance. I have no idea what these authors are talking about because the only sensible definitions for these terms are the following: Consider a field-theory...

The answer is that you simply can't make the theory generally covariant. The theory will at most be invariant under the symmetries of your (fixed) background metric. Note that this is exactly the situation in Poincare-invariant QFTs, which are studied by particle physicists all the time. To...

Diffeomorphism invariance follows whenthe theory is devoid of background geometrical data. For this reason Newton is not diffeomorphism invariant. What you mean to say is that all of the above theories can be formulated in generally covariant fashion. This is indeed correct. In the case of...

This is wrong. The first point to understand is that any physical theory can be written in a Lorentz invariant form. This includes all of the theories you mention above. I should point out that Newton is slightly different from the other theories in that it is not manifestly Lorentz...

I don't believe this is correct. The covariant conservation of energy-momentum for any field theory follows directly from diffeomorphism invariance of the matter action. The twice contracted Bianchi identity follows from diffeomorphism invariance of the kinetic term in the Einstein Hilbert action.

For future reference, the answer can be found in problem 4.1 of Becker, Becker and Shwarz.

Hi Haelfix, Thanks for your response. I do not have the equations of motion handy so I was hoping someone might know of a reference which discusses this. I believe this Lagrangian can be used to motivate the worldsheet Lagrangian in superstring theory.

Does anyone know where I can find the lagrangian for this? From memory I believe it looks something like S = \frac{1}{2} \int \frac{d\tau}{e}[\dot{X}^2 +i \dot{\psi}{\psi}-2ie\nu \dot{X} \psi] where e is the graviton and nu is the gravitino. Does anyone know of a reference that...

I think complex numbers are a bit more fundamental in QM than they are in E&M because of the interpretation of |psi|^2.

Hi Ben, That's definitely the most convincing argument I've heard so far.

I do not quite agree with you on this point. Consider as an example the action for a massless U(1) gauge field on a fixed, non-dynamical background g_{\mu\nu} S = \int d^4 x \sqrt{-g}\left(-\frac{1}{2} g^{\mu\sigma}g^{\nu \rho}F_{\mu\nu}F_{\sigma\rho} \right) Under a general coordinate...