Loop quantization from a lattice gauge theory perspective

Abstract

We present an interpretation of loop quantization in the framework of lattice gauge theory. Within this context the lack of appropriate notions of effective theories and renormalization group flow exhibit loop quantization as an incomplete framework. This interpretation includes a construction of embedded spin foam models which does not rely on the choice of any auxiliary structure (e.g. triangulation) and has the following straightforward consequences: (1) The values of the coupling constants need to be those of an UV-attractive fixed point (2) The kinematics of canonical loop quantization and embedded spin foam models are compatible (3) The weights assigned to embedded spin foams are independent of the 2-polyhedron used to regularize the path integral, $|J{|}_x=|J{|}_{x^{\prime }}$ (4) An area spectrum with edge contributions proportional to $l_{\mathrm{PL}}^2(j+1/2)$ is not compatible with embedded spin foam models and/or canonical loop quantization

11 pages, no figures; completely rewritten

References in corpus (5)

• Background Independent Quantum Gravity: A Status Report
• Spin Foam Models for Quantum Gravity
• Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
• Renormalization of Discrete Models without Background
• Spin Foam Quantization and Anomalies

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• Quantum group spin nets: refinement limit and relation to spin foams
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Geometry of C-flat connections, coarse graining and the continuum limit