Quantization of gauge fields without the path-integral formalism

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Abstract
A general treatment is given for the quantization of gauge fields which makes use of the standard field theory but avoids the path-integral formalism. For this purpose, an appropriate extension of the procedure used for the quantization of the electromagnetic field with an indefinite metric is carried out by introducing nonphysical self-commuting fields. The treatment is applied to the Yang-Mills field, Einstein's gravitational field, and the Higgs model as examples of massless and massive gauge fields. Then, the gauge-compensating terms for an arbitrary gauge field are derived, and shown to be identical to those obtained by means of the path-integral formalism.

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