On the configuration spaces of homogeneous loop quantum cosmology and loop quantum gravity - INSPIRE

DataBETA

On the configuration spaces of homogeneous loop quantum cosmology and loop quantum gravity

Sep, 2007

11 pages

e-Print:

0709.1621 [math-ph]

View in:

ADS Abstract Service

reference search44 citations

Citations per year

Abstract: (arXiv)

The set of homogeneous isotropic connections, as used in loop quantum cosmology, forms a line

l

in the space of all connections

\cal A

. This embedding, however, does not continuously extend to an embedding of the configuration space

\bar l

of homogeneous isotropic loop quantum cosmology into that of loop quantum gravity,

\bar{\cal A}

. This follows from the fact that the parallel transports for general, non-straight paths in the base manifold do not depend almost periodically on

l

. Analogous results are given for the anisotropic case.

quantum cosmology: loop space
quantum gravity: loop space
cosmological model
Hamiltonian formalism
fibre bundle: SU(2)
energy
phase space
differential equations
embedding

References(13)

Figures(0)

[1]

Ergod.Theor.Dynam.Syst. I (Encyclopaedia of Mathematical Sciences 1). -Verlag, Berlin, 1994

Dmitri V. Anosov
,
Vladimir I. Arnold

[2]

Abhay Ashtekar, Martin Bojowald, and Jerzy Lewandowski Mathematical Structure of loop quantum Grav.Cosmol. . e-print

- Adv.Theor.Math.Phys. 9 233

[2]

Mathematical structure of loop quantum cosmology

Abhay Ashtekar
(
- Penn State U. and
- Schrodinger Inst., Vienna
)
,
Martin Bojowald
(
- Penn State U. and
- Schrodinger Inst., Vienna
)
,
Jerzy Lewandowski
(
- Warsaw U. and
- Penn State U. and
- Schrodinger Inst., Vienna
)

- Adv.Theor.Math.Phys. 7 (2003) 2, 233-268
•
e-Print:
- gr-qc/0304074
•
DOI:
- 10.4310/ATMP.2003.v7.n2.a2

[3]

Background independent quantum gravity: A Status report

Abhay Ashtekar
(
)
,
Jerzy Lewandowski
(
- Warsaw U. and
- Penn State U. and
- Potsdam, Max Planck Inst. and
- Schrodinger Inst., Vienna
)

- Class.Quant.Grav. 21 (2004) R53
•
e-Print:
- gr-qc/0404018
•
DOI:
- 10.1088/0264-9381/21/15/R01

[3]

Background independent quantum gravity: A Status report

Abhay Ashtekar
(
)
,
Jerzy Lewandowski
(
- Warsaw U. and
- Penn State U. and
- Potsdam, Max Planck Inst. and
- Schrodinger Inst., Vienna
)

- Class.Quant.Grav. 21 (2004) R53
•
e-Print:
- gr-qc/0404018
•
DOI:
- 10.1088/0264-9381/21/15/R01

[4]

Harald Bohr Fastperiodische Funktionen. Verlag von Julius , Berlin, 1932

[5]

Absence of singularity in loop quantum cosmology

Martin Bojowald
(
- Penn State U.
)

- Phys.Rev.Lett. 86 (2001) 5227-5230
•
e-Print:
- gr-qc/0102069
•
DOI:
- 10.1103/PhysRevLett.86.5227

[5]

Absence of singularity in loop quantum cosmology

Martin Bojowald
(
- Penn State U.
)

- Phys.Rev.Lett. 86 (2001) 5227-5230
•
e-Print:
- gr-qc/0102069
•
DOI:
- 10.1103/PhysRevLett.86.5227

[6]

Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings

Jonathan Engle
(
- Marseille, CPT and
- Provence U. and
- Marseille U., Luminy
)

- Class.Quant.Grav. 24 (2007) 5777-5802
•
e-Print:
- gr-qc/0701132
•
DOI:
- 10.1088/0264-9381/24/23/004

[6]

Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings

Jonathan Engle
(
- Marseille, CPT and
- Provence U. and
- Marseille U., Luminy
)

- Class.Quant.Grav. 24 (2007) 5777-5802
•
e-Print:
- gr-qc/0701132
•
DOI:
- 10.1088/0264-9381/24/23/004

[7]

Christian Fleischhack Mathematische und physikalische Aspekte verallgemeinerter Eichfeldtheorien im Ashtekarprogramm (Dissertation). Universität Leipzig, 2001

[8]

of isotropic SU(2) connections on R3. in preparation

Tim A. Koslowski Holonomies

[9]

Walter Rudin Fourier Analysis on Groups. John & Sons, New York, 1990. Previous title On the physical interpretation of states in loop quantum Grav.Cosmol