sci.physics.research Google Group

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-08T08:37:24Z

Igor,
I think this may be just a question of my not using the right
terminology.
However one divides up the terminology between "Green function" and
"propagator," the calculation of the path integral has two parts to it
and that is the way in which I was using different terminologies for
each part. Specifically:

Re: Is Perfect Reversibility A Myth?

2009-11-07T09:26:11Z

As an approximation, there is nothing inconsistent.
All of physics is valid only approximately anyway; so approximations
are legitimate. In particular, one conventionally approximates the
dynamics of a part of a larger system (whether or not the latter is
assumed to be reversible) successfully as that of an irreversible

Re: Looking for Feedback on an Exercise Calculating the QED Path Integral and Greens Fucntions in Curved Spacetime with Boundary Terms

2009-11-07T09:26:11Z

. . .
I will look at the rest of this post. But, I did already look at these,
and there is nothing I am doing in
[link]
which is in any way inconsistent with these presentations. IMHO, I am
doing the same type of calculations as are being done in these papers,

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-07T09:26:11Z

Jay, I'm sorry to say this, but you are still missing a large point in
this discussion. Path integrals in curved space-time and harmonic
analysis are not contingent upon each other. You keep asking about
generalizations of Fourier transforms, so you keep getting answers
about harmonic analysis. However, none of this discussion is moving

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-06T08:42:44Z

I had meant with the open territorry the problem of a rigorous
mathematical definition of the path integral. This is an exceedingly
difficult problem, already for flat spacetime. It is unlikely to be
solved in the curved case before the flat case is understood.
On the handwaving level (i.e., in the way how all path integral stuff

Re: Looking for Feedback on an Exercise Calculating the QED Path Integral and Greens Fucntions in Curved Spacetime with Boundary Terms

2009-11-06T08:19:07Z

You're looking at everything completely the wrong way. But it would be
impossible to explain in detail just what or how until you first get
thorough background in the field, itself.
First rule of research: (1) try a problem for yourself for a while
until you get a proper feel of the layout of the territory. This will

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-06T04:00:07Z

Hi Arnold,
First, let me say that I appreciate your dialogue with both me and Igor.
It has been very helpful in trying to clarify the issues involved with
doing path integral quantization, which implicitly requires some form of
harmonic analysis, in curved spacetime. I think a separate thread might

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-06T03:58:58Z

These are indeed the only symmetric spaces, apart from Minkowski space,
that figure in general relativity. There are mor homogeneous spaces, though.
Yes, you are right; I was too quick.
Because of the big bang, there cannot be time invariance, and
realistic cosmological models with symmetry only have 3 independent

Re: Is Perfect Reversibility A Myth?

2009-11-06T03:58:42Z

Arnold Neumaier wrote on Mon, 02 Nov 2009 11:51:17 -0500:
(...)
Untrue. It is not possible to derive irreversibility from reversibility.
As Van Kampen brilliantly noted "One cannot escape from this fact by any
amount of mathematical funambulism".
The open-system approach is totally inconsistent. The subdynamics of a

Re: Looking for Feedback on an Exercise Calculating the QED Path

2009-11-04T22:59:27Z

I have that book, and have reviewed that book, and believe that this is
consistent with what I have done. I made a few tweaks and corrections
to this, in sections 1-3 of and update at
[link].
Thanks,
Jay

Re: Looking for Feedback on an Exercise Calculating the QED Path Integral and Greens Fucntions in Curved Spacetime with Boundary Terms

2009-11-04T22:59:27Z

I have uploaded an update of this exercise, to:
[link]
I made a few tweaks and corrections to this, in sections 1-3.
The new sections 4-7 get to how to calculate the propagators explicitly
in curved spacetime, and get to questions about being able to do

Re: Is Perfect Reversibility A Myth?

2009-11-04T11:39:32Z

Robert L. Oldershaw wrote on Fri, 30 Oct 2009 12:08:59 -0400:
(...)

*Any* law of physics is a mathematical ideal. One would not confound
reality with our models of her.
For certain systems the production of entropy is so low that cannot be
differentiated from zero and are explained using reversible models.

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-04T09:30:47Z

On Nov 4, 9:06 am, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>
wrote:
I do indeed have only finitely many fingers. :-)
Do you mean de Sitter or anti-de Sitter spaces, or something else? The
spatial slices of FRW cosmologies are usually treated as homogeneous
spaces. But their time evolution is put together in such a way

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-04T08:38:54Z

it was intentional. One can do it for highly symmetric space-times,
assuming that gravitational distortions that violate the symmetry can
be ignored. Then one gets a contracted approximate description in
terms of a simplified dynamics. Indeed, this is what happens in the
Post-Newton approximation, where the highly symmetric space-time is

Re: What Happens to Fourier Transforms in Curved Spacetime?

2009-11-04T08:06:30Z

You seem to have infinitely many fingers. There are many symmetric
spaces. Only upon restricting to 4 dimensions the number becomes finite.
But for a group representation approach, it is enough to have a
homogneous space (still a highly symmetric space but less than a
symmetric space), and there are infinitely many of these even in 4D