*Article* **Gauge Gravity Vacuum in Constraintless Clairaut-Type Formalism**

**Michael L. Walker 1 and Steven Duplij 2,\***

	- D-48149 Münster, Germany

**Abstract:** The gauged Lorentz theory with torsion has been argued to have an effective theory whose non-trivial background is responsible for background gravitational curvature if torsion is treated as a quantum-mechanical variable against a background of constant curvature. We use the CDG decomposition to argue that such a background can be found without including torsion. Adapting our previously published Clairaut-based treatment of QCD, we go on to study the implications for second quantisation.

**Keywords:** gravity; Clairaut equation; Cho–Duan–Ge decomposition; constraintless formalism
