denis.besak@gmx.de
Aug9-06, 04:02 AM
Darth Sidious wrote:
> > 2.As far as I understand it, the relative perturbation delta := delta
> > n/n_0 of the particle number density is not a gauge-invariant quantity,
> > right?
>
> Why not?
Well, as far as I understand it, that follows e.g. from equation (3.16)
in the review of Mukhanov/Feldman/Brandenberger. Only a combination of
the particle number density and perturbations of the metric is
gauge-invariant.
> This is the case also with the Coulomb gauge in QED. In this gauge
> you have the usual 1/r^2 potential (this is the tree-level computation,
> not including quantum corrections) from electrostatics for interaction
> between two charges. There is no retardation effect from the finite
> time it takes the interaction to travel between the two charges, and,
> therefore, you have to consider the interaction with all other charges,
> be they in the past light-cone or not. However, I would never call a
> gauge non-local. The action resulting from the elimination of all
> non-dynamical degrees of freedom is usually non-local, but this is
> another matter.
OK, maybe it is something like this. Then it has no practical
significance and I do not understand why the authors mentioned it.
> It might be that you're asking the following: suppose I compute the S-matrix for some
> non-gravitational fields on two different gravitational backgrounds.
> Is the S-matrix different in these two cases? (Note that I'm supposing
> that the notion of S-matrix is well defined in these two backgrounds.)
> In this case also, I would say the S-matrix is different. After all,
> we are dealing with two different physical systems.
This is what I meant. Usually, the formulation of QFT (action, Feynman
rules etc.) implicitly uses a Minkowski metric. My roommate and I
wonder what would be the change, e.g. in the Feynman rules, if I do not
use a Minkowski metric but a FRW metric + linear perturbations. I know
the textbook by Birrell and Davis, but it is hard to follow and
considers-except for the last chapter with some general comments on the
S-Matrix-only free fields. I do not know any book/paper that really
calculates a cross section or a decay rate in a nontrivial
gravitational background and compares it to the usual Minkowski space
result.
It would also be important for us to know under which conditions we
might be forced to consider such effects. Since we consider processes
in the very early universe (but after inflation) I am not perfectly
sure that they are negligible although no one seems to have considered
them before in this context. My first, quite naive, guess would be,
that these effects are important provided the mean free path between
two collisions becomes comparable to or even larger then the Hubble
radius. Is this correct?
> > 2.As far as I understand it, the relative perturbation delta := delta
> > n/n_0 of the particle number density is not a gauge-invariant quantity,
> > right?
>
> Why not?
Well, as far as I understand it, that follows e.g. from equation (3.16)
in the review of Mukhanov/Feldman/Brandenberger. Only a combination of
the particle number density and perturbations of the metric is
gauge-invariant.
> This is the case also with the Coulomb gauge in QED. In this gauge
> you have the usual 1/r^2 potential (this is the tree-level computation,
> not including quantum corrections) from electrostatics for interaction
> between two charges. There is no retardation effect from the finite
> time it takes the interaction to travel between the two charges, and,
> therefore, you have to consider the interaction with all other charges,
> be they in the past light-cone or not. However, I would never call a
> gauge non-local. The action resulting from the elimination of all
> non-dynamical degrees of freedom is usually non-local, but this is
> another matter.
OK, maybe it is something like this. Then it has no practical
significance and I do not understand why the authors mentioned it.
> It might be that you're asking the following: suppose I compute the S-matrix for some
> non-gravitational fields on two different gravitational backgrounds.
> Is the S-matrix different in these two cases? (Note that I'm supposing
> that the notion of S-matrix is well defined in these two backgrounds.)
> In this case also, I would say the S-matrix is different. After all,
> we are dealing with two different physical systems.
This is what I meant. Usually, the formulation of QFT (action, Feynman
rules etc.) implicitly uses a Minkowski metric. My roommate and I
wonder what would be the change, e.g. in the Feynman rules, if I do not
use a Minkowski metric but a FRW metric + linear perturbations. I know
the textbook by Birrell and Davis, but it is hard to follow and
considers-except for the last chapter with some general comments on the
S-Matrix-only free fields. I do not know any book/paper that really
calculates a cross section or a decay rate in a nontrivial
gravitational background and compares it to the usual Minkowski space
result.
It would also be important for us to know under which conditions we
might be forced to consider such effects. Since we consider processes
in the very early universe (but after inflation) I am not perfectly
sure that they are negligible although no one seems to have considered
them before in this context. My first, quite naive, guess would be,
that these effects are important provided the mean free path between
two collisions becomes comparable to or even larger then the Hubble
radius. Is this correct?