Do you know why in the quantization of $SU(2)$ Yang-Mills Gauge Theory, it is always chosen the Weyl (temporal) gauge to derive the Hamiltonian?
Is it possible to fix another gauge?
Answer
Formally, the gauge-invariant observables do not depend on the choice of gauge-fixing condition (such as, e.g., Lorenz gauge, Coulomb gauge, axial gauge, temporal gauge, etc). Similarly, the Hamiltonian can formally be gauge-fixed in any gauge.
However, it is my understanding that to avoid the Gribov problem, an algebraic (rather than a differential) gauge-fixing condition is preferred. See also the footnote on p. 15 in S. Weinberg, Quantum Theory of Fields, Vol 2.
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