Real and complex connections for canonical gravity
نویسندگان
چکیده
منابع مشابه
Quantizing Canonical Gravity in the Real Domain
There are several possibilities of formulating the classical Hamiltonian theory of pure Einstein gravity. The traditional one, proposed by Arnowitt-DeserMisner, is in terms of a canonical pair (gab, π ) of a Riemannian three-metric and its conjugate momentum. Introducing local, rotational SO(3)-degrees of freedom, one obtains a closely related formulation, based on a variable pair (E i ,K i a),...
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Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space are studied. They are based on the Lie-algebras so(1, 3) and ̃ so(3) – the loop-algebra of so(3). Although the theories are manifestly real, they can both be reformulated to show that they describe complex gravity and an infinite number of copies of complex gravity, respectively. The connection to real gravity is give...
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Upon using some special example in the homogeneous cosmological model we develop the idea that, as a result of the arbitrariness of the factor ordering in Wheeler-DeWitt equation, gauge phases can not, in general, being completely removed from the wave functional in quantum gravity. The latter may be conveniently described by means of a remnant complex term in WDW equation depending on the fact...
متن کاملInstitute for Mathematical Physics Parabolic Geometries and Canonical Cartan Connections Parabolic Geometries and Canonical Cartan Connections
Let G be a (real or complex) semisimple Lie group, whose Lie algebra g is endowed with a so called jkj{grading, i.e. a grading of the form g = g ?k g k , such that no simple factor of G is of type A 1. Let P be the subgroup corresponding to the subalgebra p = g 0 g k. The aim of this paper is to clarify the geometrical meaning of Cartan connections corresponding to the pair (G; P) and to study ...
متن کاملCanonical Gravity with Fermions
Canonical gravity in real Ashtekar–Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst's original vacuum analysis, which are explicitly displayed here. This in turn requires adaptations to the known canonical (loop) quantization of gravity coupled to fermions, which is discussed on the basis of the classical analysis.
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ژورنال
عنوان ژورنال: Classical and Quantum Gravity
سال: 1997
ISSN: 0264-9381,1361-6382
DOI: 10.1088/0264-9381/14/10/002