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| pirillo... |
 Posted: Wed Sep 09, 2009 7:00 am |
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Guest
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In some sense I feel this question is naive, but I'd like to know how
one deals with
a Lorenzian Cylinder Spacetime in both the classical and quantum
setting.
Here's what I mean: Take a 2 dimensional spacetime with the x axis
turned into
a circle and the t axis left infinitely long, now put the Lorenz flat
metric on this
in the usual way i.e., form the metric it inherits from this chart
into flat lorenz spacetime
with coordinates x, t.
Now, my question is, are lorenz transformations any meaningful in this
cylinder
space time (I figure something like boosts may be ill defined) . Also,
what are the symmetries
of this spacetime.
In the quantum setting, I want to know about the position and momentum
operators. For example,
in the flat case, there is a position operator given by multiplication
with the coordinate x,
(modulo Newton-Wigner considerations) and there are 4-momentum
operators (two in this case del_x
and del_t) . However, for the cylinder case I figure that the operator
multiplication by x no longer
exists or works, and while the momentum operators perhaps exist they
may not have proper "conjugate"'
operators for the [x, p] relations. In other words I'm suspecting the
Flat Lorez spacetime looses
some of its symmetries when "wrapped up into a cylinder" and also some
of the corresponding quantum concepts loose their meaning bit I'd like
to know to which degree this is so. |
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| ... |
| Posted: Sun Sep 13, 2009 10:06 pm |
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Guest
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pirillo <ultraman2002 at (no spam) hotmail.com> wrote:
[quote:e042dd4238]In some sense I feel this question is naive, but I'd like to know how
one deals with a Lorenzian Cylinder Spacetime in both the classical
and quantum setting.
Here's what I mean: Take a 2 dimensional spacetime with the x axis
turned into
a circle and the t axis left infinitely long, now put the Lorenz flat
metric on this in the usual way i.e., form the metric it inherits from
this chart into flat lorenz spacetime with coordinates x, t. Now,
my question is, are lorenz transformations any meaningful in this
cylinder space time (I figure something like boosts may be ill
defined) . Also, what are the symmetries of this spacetime.
[/quote:e042dd4238]
This is discussed in Dray, Am. J. Phys. 58, 822 (1990); Brans and
Stewart, Phys.Rev. D8, 1662 (1973); Uzan et al., Eur.J.Phys. 23,
277 (2002), e-Print: physics/0006039; and Barrow and Levin,
Phys.Rev. A63 (2001) 044104, arXiv:gr-qc/0101014v1. Lorentz
invariance remains a local symmetry, but it is broken globally
to just rotations and time translations.
Steve Carlip |
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