Loop Quantization of Maxwell Theory and Electric Charge Quantization

Abstract

We consider the loop quantization of Maxwell theory. A quantization of this type leads to a quantum theory in which the fundamental excitations are loop-like rather than particle-like. Each such loop plays the role of a quantized Faraday's line of electric flux. We find that the quantization depends on an arbitrary choice of a parameter e that carries the dimension of electric charge. For each value of e an electric charge that can be contained inside a bounded spatial region is automatically quantized in units of hbar/4*pi*e. The requirement of consistency with the quantization of electric charge observed in our Universe fixes a value of the, so far arbitrary, parameter e of the theory. Finally, we compare the ambiguity in the choice of parameter e with the beta-ambiguity that, as pointed by Immirzi, arises in the loop quantization of general relativity, and comment on a possible way this ambiguity can be fixed.

7 pages, Revtex, no figures, typos corrected and one reference added

References in corpus (5)

• Quantum Gravity and Regge Calculus
• The Immirzi parameter in quantum general relativity
• Quantization of Diffeomorphism-Invariant Theories with Fermions
• On the Constant that Fixes the Area Spectrum in Canonical Quantum Gravity
• Hamiltonian Reduction of Diffeomorphism Invariant Field

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