Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Master Constraint Operator in Loop Quantum Gravity   We introduce a master constraint operator $\hat{\mathbf{M}}$ 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 $\hat{\mathbf{M}}$ is positive and symmetric, and hence has its Friedrichs
self-adjoint extension. The same conclusion is tenable for an alternative
master operator $\hat{\mathbf{M'}}$, whose quadratic form coincides with the
one proposed by Thiemann. So the master constraint programme for loop quantum
gravity can be carried out in principle by employing either of the two
operators.

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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom