I've been told elsewhere that the gauge group for gravity is the general diffeomorphism group (i.e. in terms of transformations of the metric field tensor), which is what you're describing at the end there. But how does this tally with it being SL (2,C)? As I recall, SL (2,C) is related to the...
I think what you're saying here is that you have a space-time 4-vector field, and a scalar field which operates within the local 1D loops of the 5th dimension attached to every point in space-time.
What I was suggesting was that the field equation for this scalar field within a single loop of...
What I'm struggling to understand is why the curvature of the space-time hypersurface evolves; but the curvature of the higher spatial dimensions supposedly remains constant?
Also since gravity produces spatial curvature; why is it that the other forces do not?
They must've done originally...
Thanks, I think I follow that; but it still doesn't really explain why we compactify the 5th dimension?
That's why I thought it might be compactified by charge, just as space-time is distorted by mass.
I figured that since space-time curvature is non-uniform, but depends on the motion of...
I thought the Higgs field was made of superstrings/branes just like everything else?
As far as I recall, the Higgs picks out a direction in quantum state space, thus giving mass to some particle states and not others (i.e. those states aligned with the Higgs vector gain mass)? Did I remember...
In Kaluza-Klein theory, the gauge symmetries for all the fundamental
forces are mapped onto the higher spatial dimensions.
So the internal symmetries are now externalised.
Does this imply that you can extend the analogy with gravity further:
so for example, if the 5th dimension contains...
In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions:
Is the gauge group for gravity defined as the set of all possible Weyl tensors on a general 4D Riemann manifold? Which abstract group maps onto this set? Is it GL(4) or a subgroup of GL(4)? How...
In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions:
Is the gauge group for gravity defined as the group of all possible Weyl tensors on a general 4D Riemann manifold?
Is it a subgroup of GL(4)?
How do you derive the number of gravitational...
In trying to get my head round GR and quantum gravity, I'm puzzled about the following questions:
Is the gauge group for gravity defined as the group of all possible Weyl tensors on a general 4D Riemann manifold? How is this group defined in matrix algebra? Is it a subgroup of GL(4). How do...