Loop Quantization of Maxwell Theory and Electric Charge Quantization

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 tube of electric flux. We find that the quantization depends on an arbitrary choice of a parameter ε that carries the dimension of electric charge. For each value of ε an electric charge that can be contained inside a bounded spatial region is automatically quantized in units of h̄/4πε. The requirement of consistency with the quantization of electric charge observed in our Universe fixes a value of the, so far arbitrary, parameter of the theory ε. Finally, we compare the ambiguity in the choice of parameter ε with the β-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. PACS numbers: 03.70.+k, 11.15-q, 04.60.Ds Typeset using REVTEX Electronic address: [email protected] Electronic address: [email protected]