Question

Is the jacobian matrix for the definition of a tensor in Dirac's theory of everything the same as the Lorentz transformation?

Answer 1

What I mean is, when Dirac defines a tensor, he uses the general definition used in tensor calculus\[x ^{\mu'}=x^{\mu'}_{,\mu}x ^{\mu}\]Non the less I has understood Lorentz tensors were defined as\[x^{\mu'}=\Lambda^{\mu'}_{\mu}x^{\mu}\]where lambda is the tensor for Lorentz transformations. So,

1) Are Lorentz transformations in flat spacetime the same as those in curved space time?

2) Are both definition of a tensor in spacetime equivalent?

Thank you!