AMBIGUITIES IN LOOP QUANTIZATION: AREA VS. ELECTRIC CHARGE

Abstract

In this letter we compare the ambiguity that, as pointed out by Immirzi, arises in the loop quantization of general relativity with a somewhat similar ambiguity in the quantization of Maxwell theory. The "loop" quantization 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 flux line. For the case of Maxwell theory, we show that the quantization depends on an arbitrary choice of a parameter ε that carries the dimension of electric charge. For each value of ε the electric charge that can be contained inside a bounded spatial region is automatically quantized in units of ℏ/ε. The requirement of consistency with the quantization of electric charge observed in our Universe fixes a value of the, so far arbitrary, parameter ε of the theory. We compare the ambiguity in the choice of parameter ε with the β-ambiguity of quantum gravity, and comment on the possible way this ambiguity can be fixed.