Generalized group for quantum mechanics

[jfy4]

Hi,

In flat space-time, the Poincare group, is the symmetry group responsible for translations, rotations, and boosts for relativistic quantum mechanics.

For an arbitrary Einstein metric (not Minkowski space), what Lie group is responsible for coordinate transformations in relativistic quantum mechanics?

Would it be the group of projective transformations, for their geodesic preserving properties?

 

[Bill_K]

The group of coordinate transformations is an infinite-dimensional Lie group. It is described by a vector field ξ^μ(x) = x'^μ - x^μ, but its action resembles an infinite product of Lorentz groups, since it induces a Lorentz transformation ∂x^μ/∂x'^ν at each point. It is the gauge group for quantum gravity

 

[jfy4]

Are you talking about the group of diffeomorphisms?

Why is it that the group of transformations for the gravitational field is the same transformation group for particles in a gravitational field?