Related papers: Noncommutative field theory on $\mathbb{R}^3_\lamb…
While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x_i,x_j]=i theta_{ij}. Here we present new classes of (non-formal) deformed products…
We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes…
In this paper, we introduce the representation of modified $\lambda$-differential $3$-Lie algebras and define the cohomology of modified $\lambda$-differential $3$-Lie algebras with coefficients in a representation. As applications of the…
The most popular noncommutative field theories are characterized by a matrix parameter theta^(mu,nu) that violates Lorentz invariance. We consider the simplest algebra in which the theta-parameter is promoted to an operator and Lorentz…
The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n + 1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N…
Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to…
It is often expected that one cannot treat spacetime as a continuous manifold as the Planck scale is approached, because of to possible effects due to a quantum theory of gravity. There have been several proposals to model such a deviation…
We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where the space of possible Dirac operators is assigned a probability distribution. These…
Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…
We construct a deformed $C_{\lambda}$-extended Heisenberg algebra in two-dimensional space using non-commuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is…
In quantum field theories, field redefinitions are often employed to remove redundant operators in the Lagrangian, making calculations simpler and physics more evident. This technique requires some care regarding, among other things, the…
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative…
A quantum theory of noncommutative fields was recently proposed by Carmona, Cortez, Gamboa and Mendez (hep-th/0301248). The implications of the noncommutativity of the fields, intended as the requirements…
There is much discussion of scenarios where the space-time coordinates x^\mu are noncommutative. The discussion has been extended to include nontrivial anticommutation relations among spinor coordinates in superspace. A number of authors…
We consider non-local modifications of General Relativity given by a distortion function in terms of the inverse of the d'Alembert operator. The inclusion of these terms is motivated by the possibility of reproducing the current accelerated…
In this work we extend and apply a previous proposal to study noncommutative cosmology to the FRW cosmological background coupled to a scalar field, this is done in classical and quantum scenarios. In both cases noncommutativity is…
Given a symplectic manifold $M$, we may define an operad structure on the the spaces $\op^k$ of the Lagrangian submanifolds of $(\bar{M})^k\times M$ via symplectic reduction. If $M$ is also a symplectic groupoid, then its multiplication…
Let A be an associative algebra over a field, and let M be a finite family of right A-modules. Study of the noncommutative deformation functor of the family M leads to the construction of the algebra of observables and the Generalized…