TY - JOUR
T1 - Polymer and Fock representations for a scalar field
AU - Ashtekar, Abhay
AU - Lewandowski, Jerzy
AU - Sahlmann, Hanno
PY - 2003/1/7
Y1 - 2003/1/7
N2 - In loop quantum gravity, matter fields can have support only on the 'polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states cannot refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background-independent operator algebras and Hilbert spaces. Second, to make contact with low-energy physics, one has to relate this 'polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.
AB - In loop quantum gravity, matter fields can have support only on the 'polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states cannot refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background-independent operator algebras and Hilbert spaces. Second, to make contact with low-energy physics, one has to relate this 'polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.
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U2 - 10.1088/0264-9381/20/1/103
DO - 10.1088/0264-9381/20/1/103
M3 - Article
AN - SCOPUS:0037276007
SN - 0264-9381
VL - 20
SP - L11-L21
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 1
ER -