torsionneutral

torsionneutral is a term used in differential geometry and theoretical physics to describe a condition in which the torsion of an affine connection is neutralized. It is not a standard, widely adopted term, but is used informally to denote either a torsion-free geometry or a gauge in which the effects of torsion cancel in the observables of interest.

In formal terms, let M be a differentiable manifold with an affine connection ∇. The torsion tensor is T(X, Y) = ∇_X Y − ∇_Y X − [X, Y]. A torsionneutral structure means that T vanishes identically, or that there exists a contorsion tensor K such that a modified connection ∇' = ∇ + K yields a torsion-free geometry. In physics, this can correspond to choosing a frame, gauge, or representation in which torsion does not influence the dynamics, akin to working with the Levi-Civita connection in Riemannian geometry.

Usage of the term tends to be informal and context-dependent, often appearing in discussions of equivalences between torsionful and torsion-free formulations or in exploratory models where torsion is present but subsequently rendered inert for certain calculations or observers. It is most commonly associated with discussions of gauge choices, contorsion, and the relationships between curvature-based and torsion-based descriptions of geometry and gravitation.

See also: torsion, Levi-Civita connection, contorsion, teleparallelism, differential geometry.