Conservation of the stress tensor in interacting quantum field theory in curved spacetimes - INSPIRE

DataBETA

Conservation of the stress tensor in interacting quantum field theory in curved spacetimes

Stefan Hollands
(
- Chicago U., EFI and
- Chicago U.
)
,
Robert M. Wald
(
- Chicago U., EFI and
- Chicago U.
)

Apr, 2004

87 pages

Published in:

Rev.Math.Phys. 17 (2005) 227-312

e-Print:

gr-qc/0404074 [gr-qc]

DOI:

10.1142/S0129055X05002340

View in:

reference search162 citations

Citations per year

Abstract: (arXiv)

We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime. These conditions arise from a simple ``Principle of Perturbative Agreement'': For interaction Lagrangians

L_1

that are such that the interacting field theory can be constructed exactly--as occurs when

L_1

is a ``pure divergence'' or when

L_1

is at most quadratic in the field and contains no more than two derivatives--then time-ordered products must be defined so that the perturbative solution for interacting fields obtained from the Bogoliubov formula agrees with the exact solution. The conditions derived from this principle include a version of the Leibniz rule (or ``action Ward identity'') and a condition on time-ordered products that contain a factor of the free field

\phi

or the free stress-energy tensor

T_{ab}

. The main results of our paper are (1) a proof that in spacetime dimensions greater than 2, our new conditions can be consistently imposed in addition to our previously considered conditions and (2) a proof that, if they are imposed, then for {\em any} polynomial interaction Lagrangian

L_1

(with no restriction on the number of derivatives appearing in

L_1

), the stress-energy tensor

\Theta_{ab}

of the interacting theory will be conserved. Our work thereby establishes (in the context of perturbation theory) the conservation of stress-energy for an arbitrary interacting scalar field in curved spacetimes of dimension greater than 2. Our approach requires us to view time-ordered products as maps taking classical field expressions into the quantum field algebra rather than as maps taking Wick polynomials of the quantum field into the quantum field algebra.

Quantum field theory on curved space
renormalization theory
stress tensor
perturbation theory
field theory: scalar
space-time
tensor: energy-momentum
axiomatic field theory
anomaly
field theory: interaction

References(19)

Figures(0)

Gravitational Anomalies

Luis Alvarez-Gaume
(
- Harvard U.
)
,
Edward Witten
(
- Princeton U.
)

- Nucl.Phys.B 234 (1984) 269,
•
DOI:
- 10.1016/0550-3213(84)90066-X

Gauge Theories in Local Causal Perturbation Theory

Franz-Marc Boas
(
- Hamburg U.
)

e-Print:
- hep-th/0001014
•
DOI:
- 10.3204/DESY-THESIS-1999-032

WEYL COCYCLES

L. Bonora
(
- Padua U. and
- INFN, Padua
)
,
P. Pasti
(
- Padua U. and
- INFN, Padua
)
,
M. Bregola
(
- Ferrara U. and
- INFN, Bologna
)

- Class.Quant.Grav. 3 (1986) 635
•
DOI:
- 10.1088/0264-9381/3/4/018

The Microlocal spectrum condition and Wick polynomials of free fields on curved space-times

- Commun.Math.Phys. 180 (1996) 633-652
•
e-Print:
- gr-qc/9510056
•
DOI:
- 10.1007/BF02099626

Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds

Romeo Brunetti
(
- Hamburg U.
)
,
Klaus Fredenhagen
(
- Hamburg U.
)

- Commun.Math.Phys. 208 (2000) 623-661
•
e-Print:
- math-ph/9903028
•
DOI:
- 10.1007/s002200050004

The Generally covariant locality principle: A New paradigm for local quantum field theory

Romeo Brunetti
(
- Naples U. and
- INFN, Naples
)
,
Klaus Fredenhagen
(
- Hamburg U., Inst. Theor. Phys. II
)
,
Rainer Verch
(
- Gottingen U.
)

- Commun.Math.Phys. 237 (2003) 31-68
•
e-Print:
- math-ph/0112041
•
DOI:
- 10.1007/s00220-003-0815-7

Locally covariant quantum field theory

Klaus Fredenhagen
(
- Hamburg U., Inst. Theor. Phys. II
)

A Local (perturbative) construction of observables in gauge theories: The Example of QED

M. Duetsch
(
- Hamburg U.
)
,
K. Fredenhagen
(
- Hamburg U.
)

- Commun.Math.Phys. 203 (1999) 71-105
•
e-Print:
- hep-th/9807078
•
DOI:
- 10.1007/s002200050606

Algebraic quantum field theory, perturbation theory, and the loop expansion

M. Duetsch
(
- Hamburg U.
)
,
K. Fredenhagen
(
- Hamburg U.
)

- Commun.Math.Phys. 219 (2001) 5-30
•
e-Print:
- hep-th/0001129
•
DOI:
- 10.1007/PL00005563

Perturbative algebraic field theory, and deformation quantization

- Fields Inst.Commun. 30 (2001) 151-160
•
e-Print:
- hep-th/0101079

The Master Ward Identity and generalized Schwinger-Dyson equation in classical field theory

- Commun.Math.Phys. 243 (2003) 275-314
•
e-Print:
- hep-th/0211242
•
DOI:
- 10.1007/s00220-003-0968-4

Causal perturbation theory in terms of retarded products, and a proof of the action Ward identity

- Rev.Math.Phys. 16 (2004) 1291-1348
•
e-Print:
- hep-th/0403213
•
DOI:
- 10.1142/S0129055X04002266

A General PCT theorem for the operator product expansion in curved space-time

Stefan Hollands
(
- Chicago U., EFI
)

- Commun.Math.Phys. 244 (2004) 209-244
•
e-Print:
- gr-qc/0212028
•
DOI:
- 10.1007/s00220-003-0991-5

The State space of perturbative quantum field theory in curved space-times

Stefan Hollands
(
- Chicago U. and
- Chicago U., EFI
)
,
Weihua Ruan
(
- Purdue U., Hammond
)

- Annales Henri Poincare 3 (2002) 635-657
•
e-Print:
- gr-qc/0108032
•
DOI:
- 10.1007/s00023-002-8629-2

Local Wick polynomials and time ordered products of quantum fields in curved space-time

Stefan Hollands
(
- Chicago U., EFI and
- Chicago U.
)
,
Robert M. Wald
(
- Chicago U., EFI and
- Chicago U.
)

- Commun.Math.Phys. 223 (2001) 289-326
•
e-Print:
- gr-qc/0103074
•
DOI:
- 10.1007/s002200100540

Existence of local covariant time ordered products of quantum fields in curved space-time

Stefan Hollands
(
- Chicago U. and
- Chicago U., EFI
)
,
Robert M. Wald
(
- Chicago U. and
- Chicago U., EFI
)

- Commun.Math.Phys. 231 (2002) 309-345
•
e-Print:
- gr-qc/0111108
•
DOI:
- 10.1007/s00220-002-0719-y

On the renormalization group in curved space-time

Stefan Hollands
(
- Chicago U., EFI
)
,
Robert M. Wald
(
- Chicago U., EFI
)

- Commun.Math.Phys. 237 (2003) 123-160
•
e-Print:
- gr-qc/0209029
•
DOI:
- 10.1007/s00220-003-0837-1

Comments on the stress energy tensor operator in curved space-time

Valter Moretti
(
- Trento U.
)

- Commun.Math.Phys. 232 (2003) 189-221
•
e-Print:
- gr-qc/0109048
•
DOI:
- 10.1007/s00220-002-0702-7

Consequences of anomalous Ward identities

J. Wess
(
- CERN and
- Karlsruhe U.
)
,
B. Zumino
(
- CERN
)

- Phys.Lett.B 37 (1971) 95-97
•
DOI:
- 10.1016/0370-2693(71)90582-X