Why is it interesting?

Gauge fixing in classical Mechanics

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Different gauges lead to different interpretations of the theory.

• For example, when considering the QCD vacuum one usually uses the temporal gauge. This gauge makes it possible to derive the usual periodic picture of the QCD vacuum. This picture is convenient, because it allows us to understand quite pictorial what instantons are, namely tunneling processes between the vacua. However, in a different gauge like the axial gauge this picture does not emerge and there is just one non-degenerate vacuum (See the book Classical Solutions in Quantum Field Theory by Erick Weinberg)
• Another example is the Higgs mechanism. In the usually used unitary gauge, we get the now famous picture with the "Mexican Hat Potential" and the marble that runs down from the top to the new minimum, which corresponds to a non-zero vacuum expectation value of the Higgs field. However, in the temporal gauge this picture does not emerge. In this gauge the vacuum expectation value of the Higgs field is zero. (See Higgs Mechanism in the Temporal Gauge by Michael Creutz, Thomas N. Tudron and Higgs phenomenon without symmetry breaking order parameter by J. Fröhlich et. al.)

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