Abelian BF-Theory and Spherically Symmetric Electromagnetism

Abstract

Three different methods to quantize the spherically symmetric sector of electromagnetism are presented: First, it is shown that this sector is equivalent to Abelian BF-theory in four spacetime dimensions with suitable boundary conditions. This theory, in turn, is quantized by both a reduced phase space quantization and a spin network quantization. Finally, the outcome is compared with the results obtained in the recently proposed general quantum symmetry reduction scheme. In the magnetically uncharged sector, where all three approaches apply, they all lead to the same quantum theory.

21 pages, LaTeX2e, v2: minor corrections in some formulas and a new reference

References in corpus (3)

• The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
• Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
• The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant

Cited by in corpus (10)

• Loop Quantum Cosmology
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
• The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
• Coherent States for Canonical Quantum General Relativity and the Infinite Tensor Product Extension
• Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
• Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Introduction to supersymmetric spin networks