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Quantization of electromagnetic fields is investigated in the framework ofstochastic variational method (SVM). Differently from the canonicalquantization, this method does not require canonical form and quantization canbe performed directly from the gauge invariant Lagrangian. The gauge conditionis used to choose dynamically independent variables. We verify that, in theCoulomb gauge condition, SVM result is completely equivalent to the traditionalresult. On the other hand, in the Lorentz gauge condition, SVM quantization canbe performed without introducing the indefinite metric. The temporal andlongitudinal components of the gauge filed, then, behave as c-numberfunctionals affected by quantum fluctuation through the interaction withcharged matter fields. To see further the relation between SVM and thecanonical quantization, we quantize the usual gauge Lagrangian with the Fermiterm and argue a stochastic process with a negative second order correlation isintroduced to reproduce the indefinite metric.

Stochastic Variational Method as a Quantization Scheme II: Quantization of Electromagnetic Fields