The abelian sigma model in (1+1) dimensions is a field theoretical model which has a field φ : S1 → S1. An algebra of the quantum field is defined respecting the topological aspect of the model. It is shown that the zero-mode has an infinite number of inequivalent quantizations. It is also shown that when a central extension is introduced into the algebra, the winding operator and the momenta o...

We introduce twisted Steinberg algebras over a commutative unital ring $R$. These generalise and are purely algebraic analogue of Renault's groupoid C*-algebras. In particular, for each ample Hausdorff $G$ locally constant $2$-cocycle $\sigma$ on taking values in the units $R^\times$, we study algebra $A_R(G,\sigma)$ consisting compactly supported $R$-valued functions $G$, with convolution invo...

The dynamics of the 3 dimensional perfect fluid is equivalent to the motion of vortex filaments or “strings”. We study the action principle and find that it is described by the Hopf term of the nonlinear sigma model. The Poisson bracket structure is described by the loop algebra, for example, the Virasoro algebra or the analogue of O(3) current algebra. As a string theory, it is quite different...

We continue the program initiated in hep-th/0411200 and calculate the algebra of the flat currents for the string on AdS 5 × S 5 background in the light-cone gauge with κ symmetry fixed. We find that the algebra has a closed form and that the non-ultralocal terms come with a weight factor e φ(σ) that depends on the radial AdS 5 coordinate. Based on results in two-dimensional sigma models couple...

The recently derived current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor θμν , the Noether current jμ associated with the global symmetry of the theory and the composite field j appearing as the coefficient of the Schwinger term in the current algeb...

The target space M for the sigma-model appearing in theories with p-branes is considered. It is proved that M is a homogeneous space G/H. It is symmetric if and only if the U-vectors governing the sigma-model metric are either coinciding or mutually orthogonal. For nonzero noncoinciding U-vectors the Killing equations are solved. Using a block-orthogonal decomposition of the set of the U-vector...

Conventions and Notations (1) The measure space (M;M; d ) is interpreted as having M as the underly set, M the sigma algebra on M , and d the mesaure on M: If M is a metric space then M is taken as the sigma algebra generated by all its metric-open sets. (2) For two measure spaces (M;M; d ) ; (M1;M1; d 1) and (M M1;M M1; d d 1) is their product measure space. All measurs in the paper are consid...

Continuous-time Markov decision process are an important variant of labelled transition systems having nondeterminism through labels and stochasticity through exponential fire-time distributions. Nondeterministic choices are resolved using the notion of a scheduler. In this paper we characterize the class of measurable schedulers, which is the most general one, and show how a measurable schedul...

The target space M for the sigma-model appearing in theories with p-branes is considered. It is proved that M is a homogeneous space G/H . It is symmetric if and only if the U -vectors governing the sigma-model metric are either coinciding or mutually orthogonal. For nonzero noncoinciding U -vectors the Killing equations are solved. Using a block-orthogonal decomposition of the set of the U -ve...

The extension structure of the 2-dimensional current algebra of non-linear sigma models is analysed by introducing Kostant Sternberg (L, M) systems. It is found that the algebra obeys a two step extension by abelian ideals. The second step is a non-split extension of a representation of the quotient of the algebra by the first step of the extension. The cocycle which appears is analysed. Harvar...