It is shown that the SU (2) Yang-Mills theory in 3-dimensional Riemann-Cartan space-time can be completely reformulated as a gravity-like theory in terms of gauge invariant variables. The resulting Yang-Mills induced equations are found, and it is demonstrated that they can be derived from a torsion-square type of action.

Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are a priori arbitrary functions of the Cartan subalgebra generators of a Lie group which is defined on the phase space. We evaluate the corresponding path integral and find that it...

We investigate the motion of a spinning test particle in a spatially-flat FRW-type space-time in the framework of the Einstein-Cartan theory. The space-time has a torsion arising from a spinning fluid filling the space-time. We show that for spinning particles with nonzero transverse spin components, the torsion induces a precession of particle spin around the direction of the fluid spin. We al...

The operator spaces Hk n 1 ≤ k ≤ n, generalizing the row and column Hilbert spaces, and arising in the authors’ previous study of contractively complemented subspaces of C∗-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from Hk n to row or column space is...

We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural isomorphism between a moduli space of spectral data and a moduli space of differential data, each equipped with an infinite collection of commuting flows. The spect...

We construct a Frobenius structure whose intersection form coincides with the generalized Cartan matrix of \(\ell \)-Kronecker quiver \(K_{\ell }\), and underlying complex manifold is isomorphic to space stability conditions for bounded derived category finitely generated modules over path algebra \({{\mathbb {C}}}K_{\ell }\).