Mixed boundary conditions in Euclidean quantum gravity

Esposito, Giampiero; Kamenshchik, Alexander Yu.

doi:10.1088/0264-9381/12/11/004

Mixed boundary conditions in Euclidean quantum gravity

Giampiero Esposito
(
- INFN, Naples and
- Naples U.
)
,
Alexander Yu. Kamenshchik
(
- Moscow, Nucl. Safety Inst.
)

Jun 23, 1995

17 pages

Published in:

Class.Quant.Grav. 12 (1995) 2715-2722

e-Print:

gr-qc/9506092 [gr-qc]

DOI:

10.1088/0264-9381/12/11/004

Report number:

DSF-95-23

View in:

pdf

reference search32 citations

Citations per year

Abstract: (arXiv)

This paper studies a new set of mixed boundary conditions in Euclidean quantum gravity. These involve, in particular, Robin boundary conditions on the perturbed 3-metric and hence lead, by gauge invariance, to Robin conditions on the whole ghost 1-form. The corresponding trace anomaly is evaluated in the case of flat Euclidean 4-space bounded by a 3-sphere. In general, this anomaly differs from the ones resulting from other local or non-local boundary conditions studied in the recent literature.

quantum gravity: Euclidean
boundary condition
invariance: gauge
anomaly
regularization: zeta function

References(17)

Figures(0)

[1]

The Quantum State of the Universe

S.W. Hawking
(
- Cambridge U.
)

- Nucl.Phys.B 239 (1984) 257,
- Adv.Ser.Astrophys.Cosmol. 3 (1987) 236-255
•
DOI:
- 10.1016/0550-3213(84)90093-2

[2]

Quantum Gravity, Quantum Cosmology and Lorentzian Geometries

Giampiero Esposito
(
- ICTP, Trieste and
- SISSA, Trieste and
- Naples U.
)

- Lect.Notes Phys.Monogr. 12 (1992) 1-326
•
DOI:
- 10.1007/978-3-662-14495-4

[3]

Euclidean Quantum Gravity (Singapore:

Hawking S. W
,
Gibbons G. W

[4]

One loop amplitudes in Euclidean quantum gravity

Giampiero Esposito
(
- INFN, Naples and
- Naples U.
)
,
Alexander Yu Kamenshchik
(
- Moscow, Nucl. Safety Inst.
)
,
Igor V. Mishakov
(
- Moscow, Nucl. Safety Inst.
)
,
Giuseppe Pollifrone
(
- Rome U. and
- INFN, Rome
)

- Phys.Rev.D 52 (1995) 3457-3465
•
e-Print:
- gr-qc/9504016
•
DOI:
- 10.1103/PhysRevD.52.3457

[5]

The Wave Function and the Effective Action in Quantum Cosmology: Covariant Loop Expansion

A.O. Barvinsky
(
- Moscow State Pedagogical Inst.
)

- Phys.Lett.B 195 (1987) 344-348
•
DOI:
- 10.1016/0370-2693(87)90029-3

[6]

Gravitons in one loop quantum cosmology: Correspondence between covariant and noncovariant formalisms

Giampiero Esposito
(
- INFN, Naples and
- Naples U.
)
,
Alexander Yu. Kamenshchik
(
- Moscow, Nucl. Safety Inst.
)
,
Igor V. Mishakov
(
- Moscow, Nucl. Safety Inst.
)
,
Giuseppe Pollifrone
(
- INFN, Naples and
- Rome U.
)

- Phys.Rev.D 50 (1994) 6329-6337
•
e-Print:
- gr-qc/9506066
•
DOI:
- 10.1103/PhysRevD.50.6329

[7]

Mixed boundary conditions in quantum field theory

Hugh Luckock
(
- Manchester U.
)

- J.Math.Phys. 32 (1991) 1755-1766
•
DOI:
- 10.1063/1.529238

[8]

Boundary terms in the action principles of general relativity

James York
(
- North Carolina U.
)

- Found.Phys. 16 (1986) 249-257
•
DOI:
- 10.1007/BF01889475

[9]

Wave Function of the Universe

J.B. Hartle
(
- Chicago U., EFI and
- Santa Barbara, KITP
)
,
S.W. Hawking
(
- Cambridge U. and
- Santa Barbara, KITP
)

- Phys.Rev.D 28 (1983) 2960-2975,
- Adv.Ser.Astrophys.Cosmol. 3 (1987) 174-189
•
DOI:
- 10.1103/PhysRevD.28.2960

[10]

Boundary Conditions for Quantum Cosmology

- Nucl.Phys.B 341 (1990) 155-166
•
DOI:
- 10.1016/0550-3213(90)90266-G

[11]

SEMICLASSICAL WAVE FUNCTION OF THE UNIVERSE AT SMALL THREE GEOMETRIES

K. Schleich
(
- Chicago U., EFI and
- UC, Santa Barbara
)

- Phys.Rev.D 32 (1985) 1889-1898,
- Phys. Rev. D32 ( 1985) 1889-1898
•
DOI:
- 10.1103/PhysRevD.32.1889

[12]

Zeta Function Regularization of Path Integrals in Curved Space-Time

S.W. Hawking
(
- Cambridge U.
)

- Commun.Math.Phys. 55 (1977) 133
•
DOI:
- 10.1007/BF01626516

[13]

One loop quantum cosmology: Zeta function technique for the Hartle-Hawking wave function of the universe

A.O. Barvinsky
(
- Alberta U. and
- Moscow, Nucl. Safety Inst.
)
,
A.Yu. Kamenshchik
(
- Alberta U. and
- Moscow, Nucl. Safety Inst.
)
,
I.P. Karmazin
(
- Alberta U. and
- Moscow, Nucl. Safety Inst.
)

- Annals Phys. 219 (1992) 201-242
•
DOI:
- 10.1016/0003-4916(92)90347-O

[14]

Euclidean Maxwell theory in the presence of boundaries. Part 2

Giampiero Esposito
(
- INFN, Naples and
- Naples U.
)
,
Alexander Yu. Kamenshchik
(
- Moscow, Nucl. Safety Inst.
)
,
Igor V. Mishakov
(
- Moscow, Nucl. Safety Inst.
)
,
Giuseppe Pollifrone
(
- INFN, Naples and
- Rome U.
)

- Class.Quant.Grav. 11 (1994) 2939-2950
•
e-Print:
- gr-qc/9506061
•
DOI:
- 10.1088/0264-9381/11/12/009

[15]

Further functional determinants

J.S. Dowker
(
- Manchester U.
)
,
J.S. Apps
(
- Manchester U.
)

- Class.Quant.Grav. 12 (1995) 1363-1383
•
e-Print:
- hep-th/9502015
•
DOI:
- 10.1088/0264-9381/12/6/005

[16]

Zeta function determinant of the Laplace operator on the D-dimensional ball

Michael Bordag
(
- Leipzig U.
)
,
B. Geyer
(
- Leipzig U.
)
,
K. Kirsten
(
- Leipzig U.
)
,
E. Elizalde
(
- Blanes, CAS and
- Barcelona U.
)

- Commun.Math.Phys. 179 (1996) 215-234,
- Commun. Math. Phys. 179 (1996) 215-234, and Barcelona U. - UBECM-PF-95-10 (95/05,rec.Jun.) 24 p
•
e-Print:
- hep-th/9505157
•
DOI:
- 10.1007/BF02103720

[17]

On gauge invariant boundary conditions for 2-d gravity with dynamical torsion

Dmitri V. Vassilevich
(
- Vienna, Tech. U.
)

- Mod.Phys.Lett.A 10 (1995) 2239-2244,
- Mod. Phys. Lett. A10 (1995) 2239-2244, and Wien Tech. U. - TUW-95-06 (95/03,rec.Apr.) 8 p
•
e-Print:
- hep-th/9504011
•
DOI:
- 10.1142/S0217732395002398