Related papers: Some comments on the integrability of the noncommu…
We consider the generic nonanticommutative model of chiral-antichiral superfields on ${\cal N}={1\over 2}$ superspace. The model is formulated in terms of an arbitrary K\"ahlerian potential, chiral and antichiral superpotentials and can…
We study the noncommutative generalization of (euclidean) integrable models in two-dimensions, specifically the sine- and sinh-Gordon and the U(N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we…
We propose the gauged Thirring model as a natural gauge-invariant generalization of the Thirring model, four-fermion interaction of current-current type. In the strong gauge-coupling limit, the gauged Thirring model reduces to the recently…
We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field.…
In the context of integrable field theory with boundary, the integrable non-linear sigma models in two dimensions, for example, the $O(N)$, the principal chiral, the ${\rm CP}^{N-1}$ and the complex Grassmannian sigma models are discussed…
In this paper, we explore natural connections among the representations of the extended affine Lie algebra $\widehat{sl_N}(\mathbb{C}_q)$ with $\mathbb{C}_q=\mathbb{C}_q[t_0^{\pm1},t_1^{\pm1}]$ an irrational quantum 2-torus, the simple…
We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond with the symmetry algebra of $2d$ integrable models. These Lie algebras are defined by the set of infinitesimal, nonlinear, and…
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of…
The algebra of non-commutative differential geometry (NCG) on the discrete space $M_4\times Z\ma{N}$ previously proposed by the present author is improved to give the consistent explanation of the generalized gauge field as the generalized…
Gauge fields associated to the Dirac matrix algebra used with the standard quadratic gauge field Lagrangian lead to an extended gravitational Lagrangian which includes the Einstein-Hilbert one, plus quadratic, cosmological constant and…
We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in Minkowski spacetime is contained in a general Yang--Mills-like Lagrangian of metric-affine gravity (MAG), the gauge theory of the general affine group in the…
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…
The Lagrangian perturbation theory on Friedman-Lemaitre cosmologies investigated and solved up to the second order in earlier papers (Buchert 1992, Buchert \& Ehlers 1993) is evaluated up to the third order. On its basis a model for…
In this letter, we show a nilpotent matrix representation of the exterior derivative operator in noncommutative geometry (NCG), by translating the noncommutative relations of the algebraic formalization into the original one. As a result,…
By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of $N$ copies of a Lie group over some diagonal subgroup and they depend on…
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element $ds$. Its unitary representations correspond to Riemannian metrics and Spin…
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the…
A construction of conservation laws for $\sigma$-models in two dimensions is generalized in the framework of noncommutative geometry of commutative algebras. This is done by replacing the ordinary calculus of differential forms with other…
It is argued that constituent quarks live in an effective theory that possesses an approximate conformal invariance. An effective lagrangian is constructed which in the large-$\nc$ approximation incorporates Regge asymptotic constraints.…
A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper…