Related papers: Hamilton Formalism in Non-Commutative Geometry
Dickson's commutative semifields are an important class of finite division algebras. We generalise Dickson's construction of commutative division algebras by doubling both finite field extensions and central simple algebras and not…
The analogue of the Poisson bracket for the De Donder-Weyl (DW) Hamiltonian formulation of field theory is proposed. We start from the Hamilton- Poincar\'{e}-Cartan (HPC) form of the multidimensional variational calculus and define the…
In this this paper we introduce entanglement among the points in a non-commutative scheme, in addition to the tangent directions. A diagram of $A$-modules is a pair $\uc=(|\uc|,\Gamma)$ where $|\uc|={V_1,...,V_r}$ is a set of $A$-modules,…
Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. Let $P$ be a non-commutative Poisson algebra over some algebraically closed field of…
The generalized Weyl transform of index $\alpha$ is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation…
Adaptation of the Hamilton--Jacobi formalism to quantum mechanics leads to a cocycle condition, which is invariant under $D$--dimensional M\"obius transformations with Euclidean or Minkowski metrics. In this paper we aim to provide a…
Poisson sigma models are a very rich class of two-dimensional theories that includes, in particular, all 2D dilaton gravities. By using the Hamiltonian reduction method, we show that a Poisson sigma model (with a sufficiently well-behaving…
We propose a field theoretical model defined on non-commutative space-time with non-constant non-commutativity parameter $\Theta(x)$, which satisfies two main requirements: it is gauge invariant and reproduces in the commutative limit,…
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its…
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…
Based on the non-Abelian Lie algebra, a generalized geometric Lie bracket on vector space is proposed to further realize the generalized structural Poisson bracket, and then we briefly discuss the second order equations of the generalized…
The Hamiltonian analysis for a 3-dimensional connection dynamics of $\frak{so}(1,2)$, spanned by $\{L_{-+},L_{-2},L_{+2}\}$ instead of $\{L_{01}, L_{02}, L_{12}\}$, is first conducted in a Bondi-like coordinate system. The symmetry of the…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
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…
We review some recent progress in understanding the relation between a six dimensional topological Yang-Mills theory and the enumerative geometry of Calabi-Yau threefolds. The gauge theory localizes on generalized instanton solutions and is…
The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum or, equivalently, the flux of the vorticity or magnetic fields. In the Hamiltonian formalism, topological…
By considering the nonrelativistic limit of de-Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton-Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of…
A Hom-type generalization of non-commutative Poisson algebras, called non-commutative Hom-Poisson algebras, are studied. They are closed under twisting by suitable self-maps. Hom-Poisson algebras, in which the Hom-associative product is…
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382, hep-th/0611160] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the…
The notion of quantum algebras is merged with that of Lie systems in order to establish a new formalism called Poisson-Hopf algebra deformations of Lie systems. The procedure can be naturally applied to Lie systems endowed with a symplectic…