2016/07/31 by Clement Delcamp, Bianca Dittrich, Aldo Riello
Physics and Astronomy · #Black Holes and Theoretical Physics #Gauge theory #Hamiltonian lattice gauge theory #Hilbert space #Lattice field theory #Lattice gauge theory #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #Quantum entanglement #Quantum gravity #cond-mat.str-el #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep02(2017)061
72 pages
openalex created_date 2016/08/23 · openalex publication_date 2017/02/01 · arxiv created 2017/05/17 · arxiv updated 2017/05/18 · openalex updated_date 2026/08/05
We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel’d double of the gauge group, and can be readily “fused” together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2 + 1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.