Holonomy-flux spinfoam amplitude

Perini, Claudio

Holonomy-flux spinfoam amplitude

Claudio Perini
(
- Marseille, CPT
)

Nov, 2012

33 pages

e-Print:

1211.4807 [gr-qc]

View in:

ADS Abstract Service

pdf

reference search20 citations

Citations per year

Abstract: (arXiv)

We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann heat kernel coherent state transform. The new variables are classical holonomy-flux phase space variables

(h,X)\simeq \mathcal T^*SU(2)

of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection

A=\Gamma + \gamma K

, and their conjugate gravitational fluxes. For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. We briefly comment on the possibility to use the alternative flipped classical limit.

Note:

33 pages

04.60.Gw
04.60.Nc
04.60.Pp
spin: foam
space-time: classical
quantum gravity: loop space
heat kernel
Immirzi parameter
coherent state
holomorphic

References(46)

Figures(0)

[1]

LQG vertex with finite Immirzi parameter

Jonathan Engle
(
- Marseille, CPT
)
,
Etera Livine
(
- Lyon, Ecole Normale Superieure
)
,
Roberto Pereira
(
- Marseille, CPT
)
,
Carlo Rovelli
(
- Marseille, CPT
)

- Nucl.Phys.B 799 (2008) 136-149
•
e-Print:
- 0711.0146
•
DOI:
- 10.1016/j.nuclphysb.2008.02.018

[2]

Spinfoams in the holomorphic representation

Eugenio Bianchi
(
- Marseille, CPT
)
,
Elena Magliaro
(
- Marseille, CPT
)
,
Claudio Perini
(
- Marseille, CPT and
- Rome U.
)

- Phys.Rev.D 82 (2010) 124031
•
e-Print:
- 1004.4550
•
DOI:
- 10.1103/PhysRevD.82.124031

[3]

The Segal-Bargmann Coherent State Transform for Compact Lie Groups

Brian C. Hall

- J.Funct.Anal. 122 (1994) 103

[4]

Gauge field theory coherent states (GCS): 3. Ehrenfest theorems

- Class.Quant.Grav. 18 (2001) 4629-4682
•
e-Print:
- hep-th/0005234
•
DOI:
- 10.1088/0264-9381/18/21/315

[5]

Towards the QFT on curved space-time limit of QGR. 1. A General scheme

- Class.Quant.Grav. 23 (2006) 867-908
•
e-Print:
- gr-qc/0207030
•
DOI:
- 10.1088/0264-9381/23/3/019

[6]

Towards the QFT on curved space-time limit of QGR. 2. A Concrete implementation

- Class.Quant.Grav. 23 (2006) 909-954
•
e-Print:
- gr-qc/0207031
•
DOI:
- 10.1088/0264-9381/23/3/020

[7]

Approximating the physical inner product of Loop Quantum Cosmology

- Class.Quant.Grav. 24 (2007) 2109-2138
•
e-Print:
- gr-qc/0607075
•
DOI:
- 10.1088/0264-9381/24/8/011

[8]

Coherent state transforms for spaces of connections

- J.Funct.Anal. 135 (1996) 519-551
•
e-Print:
- gr-qc/9412014
•
DOI:
- 10.1006/jfan.1996.0018

[9]

Coherent spin-networks

Eugenio Bianchi
(
- Marseille, CPT
)
,
Elena Magliaro
(
- Marseille, CPT
)
,
Claudio Perini
(
- Marseille, CPT and
- Rome III U.
)

- Phys.Rev.D 82 (2010) 024012
•
e-Print:
- 0912.4054
•
DOI:
- 10.1103/PhysRevD.82.024012

[10]

Towards Spinfoam Cosmology

Eugenio Bianchi
(
- Marseille, CPT
)
,
Carlo Rovelli
(
- Marseille, CPT
)
,
Francesca Vidotto
(
- Marseille, CPT and
- Pavia U. and
- INFN, Pavia
)

- Phys.Rev.D 82 (2010) 084035
•
e-Print:
- 1003.3483
•
DOI:
- 10.1103/PhysRevD.82.084035

[11]

Coherent states for FLRW space-times in loop quantum gravity

Elena Magliaro
(
- Penn State U.
)
,
Antonino Marciano
(
- Haverford Coll.
)
,
Claudio Perini
(
- Penn State U.
)

- Phys.Rev.D 83 (2011) 044029
•
e-Print:
- 1011.5676
•
DOI:
- 10.1103/PhysRevD.83.044029

[12]

Cosmological constant in spinfoam cosmology

Eugenio Bianchi
(
- Marseille, CPT
)
,
Thomas Krajewski
(
- Marseille, CPT and
- Orsay, LPT
)
,
Carlo Rovelli
(
- Marseille, CPT
)
,
Francesca Vidotto
(
- Marseille, CPT and
- Pavia U. and
- INFN, Pavia
)

- Phys.Rev.D 83 (2011) 104015
•
e-Print:
- 1101.4049
•
DOI:
- 10.1103/PhysRevD.83.104015

[13]

First-order quantum-gravitational correction from covariant, holomorphic spinfoam cosmology

Christian Roken
(
- Marseille, CPT
)

- Int.J.Mod.Phys.D 22 (2015) 02, 1350005,
- Int.J.Mod.Phys.D 22 (2015) 02, 1592003 (erratum)
•
e-Print:
- 1011.3335
•
DOI:
- 10.1142/S0218271813500053