This paper presents a new event generator, ALPGEN, dedicated to the study of multiparton hard processes in hadronic collisions. The code performs, at the leading order in QCD and EW interactions, the calculation of the exact matrix elements for a large set of parton-level processes of interest in the study of the Tevatron and LHC data. The current version of the code describes the following final states: (W→f')Q+N jets (Q being a heavy quark, and f = l,q), with N ≤ 4;(Z/γ*→f)Q+N jets (f = l,ν), with N ≤ 4; W→f')+charm+N jets (f = l,q,N ≤ 5;W→f')+N jets (f = l,q and Z/γ*→f)+N jets (f = l,ν), with N ≤ 6; nW+mZ+lH+N jets, with n+m+l+N ≤ 8, N ≤ 3, including all 2-fermion decay modes of W and Z bosons, with spin correlations; Q+N jets, with t→bf' decays and relative spin correlations included where relevant, and N ≤ 6; QQ''+N jets, with Q and Q' heavy quarks (possibly equal) and N ≤ 4; HQ+N jets, with t→bf' decays and relative spin correlations included where relevant and N ≤ 4; N jets, with N ≤ 6. Parton-level events are generated, providing full information on their colour and flavour structure, enabling the evolution of the partons into fully hadronised final states.

/pdf/alpgen-a-generator-for-hard-multiparton-processes-in-4tuthlh5y0.pdf

ALPGEN, a generator for hard multiparton processes in hadronic collisions

It is shown that in a natural way there are precisely sixteen classes of almost Hermitian manifolds.

https://link.springer.com/content/pdf/10.1007/BF01796539.pdf

The sixteen classes of almost Hermitian manifolds and their linear invariants

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does not satisfy the Jacobi identity except on certain subspaces. In this paper we systematize the properties of this bracket in the definition of a Courant algebroid. This structure on a vector bundle $E\rightarrow M$, consists of an antisymmetric bracket on the sections of $E$ whose ``Jacobi anomaly'' has an explicit expression in terms of a bundle map $E\rightarrow TM$ and a field of symmetric bilinear forms on $E$. When $M$ is a point, the definition reduces to that of a Lie algebra carrying an invariant nondegenerate symmetric bilinear form. For any Lie bialgebroid $(A,A^{*})$ over $M$ (a notion defined by Mackenzie and Xu), there is a natural Courant algebroid structure on $A\oplus A^{*}$ which is the Drinfel'd double of a Lie bialgebra when $M$ is a point. Conversely, if $A$ and $A^*$ are complementary isotropic subbundles of a Courant algebroid $E$, closed under the bracket (such a bundle, with dimension half that of $E$, is called a Dirac structure), there is a natural Lie bialgebroid structure on $(A,A^{*})$ whose double is isomorphic to $E$. The theory of Manin triples is thereby extended from Lie algebras to Lie algebroids. Our work gives a new approach to bihamiltonian structures and a new way of combining two Poisson structures to obtain a third one. We also take some tentative steps toward generalizing Drinfel'd's theory of Poisson homogeneous spaces from groups to groupoids.

/pdf/manin-triples-for-lie-bialgebroids-2do61urqws.pdf

Manin Triples for Lie Bialgebroids

Classical and quantum mechanics of the damped harmonic oscillator

UNIVERSAL ENVELOPING ALGEBRAS Algebraic constructions The Poincare-Birkhoff-Witt theorem POISSON GEOMETRY Poisson structures Normal forms Local Poisson geometry POISSON CATEGORY Poisson maps Hamiltonian actions DUAL PAIRS Operator algebras Dual pairs in Poisson geometry Examples of symplectic realizations GENERALIZED FUNCTIONS Group algebras Densities GROUPOIDS Groupoids Groupoid algebras Extended groupoid algebras ALGEBROIDS Lie algebroids Examples of Lie algebroids Differential geometry for Lie algebroids DEFORMATIONS OF ALGEBRAS OF FUNCTIONS Algebraic deformation theory Weyl algebras Deformation quantization.

/pdf/geometric-models-for-noncommutative-algebras-3yqtarz6qx.pdf

Geometric Models for Noncommutative Algebras

In the paper, one establishes the decomposition of the space of tensors which have the symmetries of the curvature of a torsionless symplectic connection into Sp (n)-irreducible components. This leads to three interesting classes of symplectic connections: flat, Ricci flat, and similar to the Levi-Civita connections of Kahler manifolds with constant holomorphic sectional curvature (we call them connections with reducible curvature). A symplectic manifold with two transversal polarizations has a canonical symplectic connection, and we study properties that are encountered if this canonical connection belongs to the classes mentioned above. For instance, in the reducible case we can compute the Pontrjagin classes, and these will be zero if the polarizations are real, etc. If the polarizations are real and there exist points where they are either singular or nontransversal, one has residues in the sense ofLehmann [L], which should be expected to play an interesting role in symplectic geometry.

Symplectic curvature tensors

In the paper, we establish some conditions which ensure one of the following: (i) the existence of the pullback of the quantization bundle of a Poisson manifold to a quantization bundle of a symplectic leaf, (ii) the existence of the projection of a quantization bundle from a presymplectic realization of a Poisson manifold to the manifold or to its symplectic leaves. The main case is that of an isotropic realization. The paper ends by a discussion of the notion of a polarization of a Poisson manifold.

On the geometric quantization of the symplectic leaves of Poisson manifolds

We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.

/pdf/the-bv-algebra-of-a-jacobi-manifold-t6yhvkuhxs.pdf

The BV-algebra of a Jacobi manifold

This is an expository paper. In it, the Poisson—Nijenhuis structures are motivated and defined in the general algebraic framework of Gel’fand and Dorfman. Then, in the particular case of Lie algebroids and differentiable manifolds, the Poisson—Nijenhuis structures are related to the notion of a complementary 2-form, that has been introduced and studied by the author in [20], and several examples of complementary forms and Poisson—Nijenhuis manifolds are given.

A Lecture on Poisson—Nijenhuis Structures

A locally conformal symplectic (l.c.s.) manifold is a pair (M2n,fl) where M2n(n > i) is a connected differentiable manifold, and a nondegenerate 2-form on M such that M k9 Us (Us- open subsets) /U e , o U s -IR, d O. Equivalently, d ^ .q for some closed 1-form . L.c.s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetlc canonical transformations. The paper discusses first Hamiltonian vector fields, and infinitesimal automorphisms (i.a.) on l.c.s, manifolds. If (M,) has an i.a. X such that (X) 0, we say that M is of the first kind and assumes the particular form de ^ e Such an M is a 2-contact manifold with the structure forms (,e), and it has a vertical 2-dlmensional foliation V. If V is regular, we can give a flbration theorem which shows that M is a T2-principal bundle over a symplectlc manifold. Particularly, 9 is regular for some homogeneous l.c.s, manifolds, and this leads to a general con- struction of compact homogeneous l.c.s, manifolds. Various related geometric results, including reductivity theorems for Lie algebras of i.a. are also given. Most of the proofs are adaptations of corresponding proofs in symplectlc and contact geometry. The paper ends with an Appendix which states an analogous fibratlon theorem in Riemannlan

/pdf/locally-conformal-symplectic-manifolds-2caxxy01r0.pdf

Locally conformal symplectic manifolds

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