TWO-LOOP APPROACH TO THE EFFECTIVE ACTION IN QUANTUM GRAVITY

1992 ◽  
Vol 07 (14) ◽  
pp. 3203-3233 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
S. D. ODINTSOV ◽  
O. A. FONAREV
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Minkowski Space ◽  
Effective Action ◽  
Dimensional Regularization ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
Metric Tensor ◽  
First Time

For the first time we present the general formalism and results of calculation of the two-loop effective action in Einstein quantum gravity on the background MN × Tk, where MN is Minkowski space and Tk is a k-dimensional torus. We discuss the case of a zero cosmological constant as well as of a nonzero one. The method of calculating variations of the action on a metric tensor and the technique of calculating momentum integrals in dimensional regularization are presented. Some applications to spontaneous compactification are discussed, as well as some prospects.

SPONTANEOUS SUPERSYMMETRY BREAKING AND EFFECTIVE ACTION IN SUPERSYMMETRICAL KALUZA-KLEIN THEORIES AND STRINGS

1989 ◽  
Vol 04 (17) ◽  
pp. 4337-4351 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
S. D. ODINTSOV
Keyword(s):  
Minkowski Space ◽  
Supersymmetry Breaking ◽  
Effective Action ◽  
Vacuum Energy ◽  
Nonzero Temperature ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
Curved Space ◽  
The One ◽  
Kaluza Klein

The one-loop effective action (EA) for arbitrary supersymmetric theory with broken supersymmetry on the background Rb × Td−n, where Rn, Td are n-dimensional curved space-time and d-dimensional torus, is obtained. Vilcovisky-De Witt EA in d = 5 (super)gravity on the background R4 × T1 at nonzero temperature is calculated with accuracy to linear curvature terms. Vacuum energy for open and closed superstrings with broken supersymmetry on the background M4 × T6, where M4 is Minkowski space, is also obtained. The question of the possibility of spontaneous compactification in models under consideration is analyzed.

THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

scholarly journals SPONTANEOUS COMPACTIFICATION IN 2D INDUCED QUANTUM GRAVITY

1992 ◽  
Vol 07 (26) ◽  
pp. 2369-2376 ◽  
Author(s):  
E. ELIZALDE ◽  
S. D. ODINTSOV
Keyword(s):  
Quantum Gravity ◽  
Effective Action ◽  
Spontaneous Compactification

Spontaneous compactification – on a R1 × S1 background – in 2D induced quantum gravity (considered as a toy model for more fundamental quantum gravity) is analyzed in the gauge-independent effective action formalism. It is shown that such compactification is stable, in contradistinction to multidimensional quantum gravity on a RD × S1(D > 2) background – which is known to be one-loop unstable.

scholarly journals Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 287 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Gravitational Field ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Proper Time ◽  
Theoretical Background ◽  
Space Time ◽  
Einstein Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Covariant Quantum

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

scholarly journals Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 531 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Space Time ◽  
Energy Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Screening Effect ◽  
Periodic Perturbations ◽  
Desitter Space

Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out.

scholarly journals MEASUREMENTS AND INFORMATION IN SPIN FOAM MODELS

2012 ◽  
Vol 27 (28) ◽  
pp. 1250164
Author(s):  
J. MANUEL GARCÍA-ISLAS
Keyword(s):  
Information Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Shannon Entropy ◽  
Three Dimensional ◽  
Spin Network ◽  
Spin Foam Models ◽  
Foam Model ◽  
Spin Foam Model ◽  
Spin Foam

In the three-dimensional spin foam model of quantum gravity with a cosmological constant, there exists a set of observables associated with spin network graphs. A set of probabilities is calculated from these observables, and hence the associated Shannon entropy can be defined. We present the Shannon entropy associated with these observables and find some interesting bounded inequalities. The problem relates measurements, entropy and information theory in a simple way which we explain.

scholarly journals EFFECTIVE THEORY FOR QUANTUM GRAVITY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342014 ◽  
Author(s):  
XAVIER CALMET
Keyword(s):  
Higgs Boson ◽  
Quantum Gravity ◽  
Effective Action ◽  
Binary Systems ◽  
Ricci Scalar ◽  
Effective Theory ◽  
Nonminimal Coupling ◽  
Order Unity

In this paper, we discuss an effective theory for quantum gravity and discuss the bounds on the parameters of this effective action. In particular, we show that measurement in pulsars binary systems are unlikely to improve the bounds on the coefficients of the R2 and RμνRμν terms obtained from probes of Newton's potential performed on Earth. Furthermore, we argue that if the coefficients of these terms are induced by quantum gravity, they should be at most of order unity since R2 and RμνRμν are dimension four operators. The same applies to the nonminimal coupling of the Higgs boson to the Ricci scalar.

scholarly journals TIME, VACUUM ENERGY, AND THE COSMOLOGICAL CONSTANT

2009 ◽  
Vol 18 (14) ◽  
pp. 2265-2268 ◽  
Author(s):  
VIQAR HUSAIN
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Cosmological Constant Problem ◽  
Problem Of Time ◽  
The Relationship

We describe a link between the cosmological constant problem and the problem of time in quantum gravity. This arises from examining the relationship between the cosmological constant and vacuum energy in light of nonperturbative formulations of quantum gravity.

scholarly journals CONSTRAINTS IN QUANTUM GEOMETRODYNAMICS

2004 ◽  
Vol 19 (10) ◽  
pp. 1609-1638 ◽  
Author(s):  
ADRIAN P. GENTLE ◽  
NATHAN D. GEORGE ◽  
ARKADY KHEYFETS ◽  
WARNER A. MILLER
Keyword(s):  
Quantum Gravity ◽  
General Setting ◽  
Square Root ◽  
Dynamical Equations ◽  
Dynamic Content ◽  
Quantization Formalism ◽  
Canonical Quantum Gravity ◽  
First Time ◽  
Quantum Geometrodynamics ◽  
Canonical Quantum

We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3-geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the traditional dynamical equations obsolete. Quantization of the constraints in both the Dirac and ADM square root Hamiltonian approaches leads to the well known problems of time evolution. These problems of time are of both an interpretational and technical nature. In contrast, the geometrodynamic quantization procedure on the superspace of the true dynamical variables separates the issues of quantization from the enforcement of the constraints. The resulting theory takes into account states that are off-shell with respect to the constraints, and thus avoids the problems of time. We develop, for the first time, the geometrodynamic quantization formalism in a general setting and show that it retains all essential features previously illustrated in the context of homogeneous cosmologies.

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