scholarly journals First-order action and Euclidean quantum gravity

2009 ◽  
Vol 26 (14) ◽  
pp. 145004 ◽  
Author(s):  
Tomáš Liko ◽  
David Sloan
Keyword(s):  
Quantum Gravity ◽  
First Order

scholarly journals Quantum Gravity at the Corner

Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 107 ◽  
Author(s):  
Laurent Freidel ◽  
Alejandro Perez
Keyword(s):  
Quantum Gravity ◽  
Symplectic Form ◽  
Direct Application ◽  
Quantum Geometry ◽  
Quantum Level ◽  
Gravitational System ◽  
Gauge Transformations ◽  
First Order ◽  
Conformal Field ◽  
First Time

We investigate the quantum geometry of a 2d surface S bounding the Cauchy slices of a 4d gravitational system. We investigate in detail for the first time the boundary symplectic current that naturally arises in the first-order formulation of general relativity in terms of the Ashtekar–Barbero connection. This current is proportional to the simplest quadratic form constructed out of the pull back to S of the triad field. We show that the would-be-gauge degrees of freedo arising from S U ( 2 ) gauge transformations plus diffeomorphisms tangent to the boundary are entirely described by the boundary 2-dimensional symplectic form, and give rise to a representation at each point of S of S L ( 2 , R ) × S U ( 2 ) . Independently of the connection with gravity, this system is very simple and rich at the quantum level, with possible connections with conformal field theory in 2d. A direct application of the quantum theory is modelling of the black horizons in quantum gravity.

scholarly journals A First Approach to Loop Quantum Gravity in the Momentum Representation

2019 ◽  
pp. 1-8
Author(s):  
W. F. Chagas-Filho
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Classical System ◽  
Momentum Representation ◽  
First Order

We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations that can be interpreted as describing quantum gravity in the momentum representation.

scholarly journals First order formalism for quantum gravity

1987 ◽  
Author(s):  
M. Gleiser ◽  
R. Holman ◽  
N.P. Neto
Keyword(s):  
Quantum Gravity ◽  
First Order

scholarly journals A NOVEL SPIN-STATISTICS THEOREM IN (2 + 1)DCHERN–SIMONS GRAVITY

2001 ◽  
Vol 16 (20) ◽  
pp. 1335-1347 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
E. BATISTA ◽  
I. P. COSTA E SILVA ◽  
P. TEOTONIO-SOBRINHO
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Canonical Formalism ◽  
Irreducible Representations ◽  
First Order ◽  
Algebraic Description ◽  
Spin And Statistics

It has been known for some time that topological geons in quantum gravity may lead to a complete violation of the canonical spin-statistics relation: There may be no connection between spin and statistics for a pair of geons. We present an algebraic description of quantum gravity in a (2 + 1) D manifold of the form Σ × ℝ, based on the first-order canonical formalism of general relativity. We identify a certain algebra describing the system, and obtain its irreducible representations. We then show that although the usual spin-statistics theorem is not valid, statistics is completely determined by spin for each of these irreducible representations, provided one of the labels of these representations, which we call flux, is superselected. We argue that this is indeed the case. Hence, a new spin-statistics theorem can be formulated.

scholarly journals Quantum gravity, renormalizability and diffeomorphism invariance

2018 ◽  
Vol 5 (4) ◽  
Author(s):  
Tim Morris
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Renormalization Group ◽  
Quantum Gravity ◽  
Master Equation ◽  
Conformal Factor ◽  
Quantum Master Equation ◽  
First Order ◽  
Diffeomorphism Invariance ◽  
Brst Cohomology

We show that the Wilsonian renormalization group (RG) provides a natural regularisation of the Quantum Master Equation such that to first order the BRST algebra closes on local functionals spanned by the eigenoperators with constant couplings. We then apply this to quantum gravity. Around the Gaussian fixed point, RG properties of the conformal factor of the metric allow the construction of a Hilbert space \Ll of renormalizable interactions, non-perturbative in \hbarℏ, and involving arbitrarily high powers of the gravitational fluctuations. We show that diffeomorphism invariance is violated for interactions that lie inside \Ll, in the sense that only a trivial quantum BRST cohomology exists for interactions at first order in the couplings. However by taking a limit to the boundary of \Ll, the couplings can be constrained to recover Newton’s constant, and standard realisations of diffeomorphism invariance, whilst retaining renormalizability. The limits are sufficiently flexible to allow this also at higher orders. This leaves open a number of questions that should find their answer at second order. We develop much of the framework that will allow these calculations to be performed.

scholarly journals First order formalism for quantum gravity

1987 ◽  
Vol 294 ◽  
pp. 1164-1179 ◽  
Author(s):  
Marcelo Gleiser ◽  
Richard Holman ◽  
Nelson P. Neto
Keyword(s):  
Quantum Gravity ◽  
First Order

REIDEMEISTER TORSION AND SIMPLICIAL QUANTUM GRAVITY

1993 ◽  
Vol 08 (11) ◽  
pp. 1933-1980 ◽  
Author(s):  
M. CARFORA ◽  
A. MARZUOLI
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Three Dimensional ◽  
Gaussian Model ◽  
Coupling Constants ◽  
First Order ◽  
Homotopy Types ◽  
First Order Phase Transition ◽  
Homology Manifolds ◽  
First Order Phase

We show that three-dimensional simplicial quantum gravity, as described by dynamically triangulated manifolds, is connected with a Gaussian model determined by the simple homotopy types of the underlying manifolds. By exploiting this result it is shown that the partition function of three-dimensional simplicial quantum gravity is well defined in a convex region in the plane of the gravitational and cosmological coupling constants. Such a region is determined by the Reidemeister–Franz torsion invariants associated with orthogonal representations of the fundamental groups of the set of manifolds considered. The system shows a critical behavior and undergoes a first order phase transition at a well-defined value of the couplings, again determined by the torsion invariants. On the critical line the partition function can be explicitly related to a Gaussian measure on the general linear group GL (∞, R), showing evidence of a well-defined thermodynamical limit of the theory, with a stable (vacuum) configuration corresponding to three-dimensional (homology) manifolds. The first order nature of the transition yielding such a configuration seems to support the belief in the absence of a continuum limit of the theory. More generally, the approach presented here provides further analytical support for the picture of three-dimensional simplicial quantum gravity which has been abstracted from numerical simulations.

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