caa a22 4500 44538638X CHVBK 20180317143033.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10714-011-1252-0 doi (NATIONALLICENCE)springer-10.1007/s10714-011-1252-0 Quantum scalar field in quantum gravity: the propagator and Lorentz invariance in the spherically symmetric case [Elektronische Daten] [Rodolfo Gambini, Jorge Pullin, Saeed Rastgoo] We recently studied gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since there are local degrees of freedom one faces the "problem of dynamics”. We attack it using the "uniform discretization technique”. We find the quantum state that minimizes the value of the master constraint for the case of weak fields and curvatures. The state has the form of a direct product of Gaussians for the gravitational variables times a modified Fock state for the scalar field. In this paper we do three things. First, we verify that the previous state also yields a small value of the master constraint when one polymerizes the scalar field in addition to the gravitational variables. We then study the propagators for the polymerized scalar field in flat space-time using the previously considered ground state in the low energy limit. We discuss the issue of the Lorentz invariance of the whole approach. We note that if one uses real clocks to describe the system, Lorentz invariance violations are small. We discuss the implications of these results in the light of Hořava's Gravity at the Lifshitz point and of the argument about potential large Lorentz violations in interacting field theories of Collins etal. Springer Science+Business Media, LLC, 2011 Loop quantum gravity nationallicence Scalar field nationallicence Lorentz invariance nationallicence Gambini Rodolfo Instituto de Física, Facultad de Ciencias, Iguá 4225, esq. Mataojo, Montevideo, Uruguay aut Pullin Jorge Department of Physics and Astronomy, Louisiana State University, 70803-4001, Baton Rouge, LA, USA aut Rastgoo Saeed Instituto de Física, Facultad de Ciencias, Iguá 4225, esq. Mataojo, Montevideo, Uruguay aut General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/12(2011-12-01), 3569-3592 0001-7701 43:12<3569 2011 43 10714 https://doi.org/10.1007/s10714-011-1252-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-011-1252-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gambini Rodolfo Instituto de Física, Facultad de Ciencias, Iguá 4225, esq. Mataojo, Montevideo, Uruguay aut NATIONALLICENCE 700 1- Pullin Jorge Department of Physics and Astronomy, Louisiana State University, 70803-4001, Baton Rouge, LA, USA aut NATIONALLICENCE 700 1- Rastgoo Saeed Instituto de Física, Facultad de Ciencias, Iguá 4225, esq. Mataojo, Montevideo, Uruguay aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/12(2011-12-01), 3569-3592 0001-7701 43:12<3569 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer