Gauge fixing and canonical quantization

Rotating frames and gauge invariance in three-dimensional many-body quantum systems

“…Since both l and s are constants of motion, this constraint is clearly consistent with the dynamics. We see that the quantized theory in the ξ = 0 gauge is completely analogous to Yang-Mills theories in the temporal gauge [6,17,18]. The constraint fixing the value of j, in particular, is the equivalent of the non-Abelian Gauss law.…”

“…We denote dynamical quantities in this gauge by capital letters, in particular the position vectors R α , E and the angular momenta L and S, as opposed to the corresponding quantities in the gauge ξ = 0 (the laboratory frame) which are denoted r α , e, l, s. Thus S a ({R α }) = 0 but, in general, S a ({r α }) = 0. The gauge conditions (8) select a reference frame rotating so that the linear combinations of coordinates S a vanish for all t. If we choose, for instance, all coefficients in (8) vanishing except for Γ 11Y = Γ 21Z = Γ 32Y = 1, the coordinate frame must rotate together with particles 1 and 2 so that 1 is on the X axis and 2 on the X − Z plane for all t. The formalism in these linear gauges is entirely analogous to that of non-Abelian Yang-Mills theories in linear non-covariant gauges, such as the Coulomb or axial gauges, in which the fields are also constrained by linear relations [6](see also [3,17,18]). …”

Instantons and Gribov copies in the maximally Abelian gauge

“…Let us make this statement slightly more rigorous. To this end we modify an argument used in [14,32] for background type gauges. First of all we note that together with the configuration (A , A ⊥ ) also the scaled configuration (A , λA ⊥ ), with λ some (positive real) parameter, will be in the MAG.…”

On unconstrained SU(2) gluodynamics with theta angle

“…The standard way in the Hamiltonian approach to proceed further, is to perform a partial integration in the last term in expression (2.6) for the canonical Hamiltonian 8) where according to the Gauss theorem the surface integral is over the two-dimensional closed surface covering the three-dimensional volume V R ( for simplicity we assume that it is a ball with radius R ). Supposing that…”