Hamiltonian constraint in polymer parametrized field theory

Laddha, Alok; Varadarajan, Madhavan

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/4052

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DC Field	Value	Language
dc.contributor.author	Laddha, Alok	-
dc.contributor.author	Varadarajan, Madhavan	-
dc.date.accessioned	2011-08-01T05:54:19Z	-
dc.date.available	2011-08-01T05:54:19Z	-
dc.date.issued	2011-01-25	-
dc.identifier.citation	Physical Review D, 2011, Vol.83, p25019	en
dc.identifier.issn	1550-2368 (Online)	-
dc.identifier.issn	1550-7998	-
dc.identifier.uri	http://hdl.handle.net/2289/4052	-
dc.description	Open Access	en
dc.description.abstract	Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type “polymer” representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.	en
dc.language.iso	en	en
dc.publisher	American Physical Society	en
dc.relation.uri	http://arxiv.org/abs/1011.2463	en
dc.relation.uri	http://dx.doi.org/10.1103/PhysRevD.83.025019	en
dc.relation.uri	http://adsabs.harvard.edu/abs/2011PhRvD..83b5019L	en
dc.rights	2011 The American Physical Society	en
dc.title	Hamiltonian constraint in polymer parametrized field theory	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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