Matrix elements of Thiemann's Hamiltonian constraint in loop quantum gravity
نویسندگان
چکیده
منابع مشابه
Matrix Elements of Thiemann’s Hamiltonian Constraint in Loop Quantum Gravity
We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann’s version of the constraint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques from the recoupling theory of colored knots and li...
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We introduce a master constraint operator M̂ densely defined in the diffeomorphism invariant Hilbert space in loop quantum gravity, which corresponds classically to the master constraint in the programme. It is shown that M̂ is positive and symmetric, and hence has its Friedrichs self-adjoint extension. The same conclusion is tenable for an alternative master operator M̂′, whose quadratic form coi...
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The Hamiltonian constraint remains the major unsolved problem in Loop Quantum Gravity (LQG). Seven years ago a mathematically consistent candidate Hamiltonian constraint has been proposed but there are still several unsettled questions which concern the algebra of commutators among smeared Hamiltonian constraints which must be faced in order to make progress. In this paper we propose a solution...
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ژورنال
عنوان ژورنال: Classical and Quantum Gravity
سال: 1997
ISSN: 0264-9381,1361-6382
DOI: 10.1088/0264-9381/14/10/008