Yang–Mills analogues of the Immirzi ambiguity

Several new insights into the canonical quantization of general relativity have been acquired using Ashtekar-like variables [1]. Originally, this consisted in basing the theory on a canonical pair formed by a set of (densitized) triads Ẽ i , and a (complex) SU(2) connection A i a ≡ Γ i a + iK i a, where Γ i a is the spin connection compatible with the triads and K a = KabE bi where Kab is the extrinsic curvature. In terms of these variables, the constraints of the theory became a Yang–Millslike Gauss law, plus expressions for the traditional vector and Hamiltonian constraints,