Mehmet Tekkoyun
In this study, Clifford Kaehler analogue of Lagrangian dynamics is introduced. Also,the some geometrical and physical results over the obtained Clifford Kaehler dynamical systems are discussed.
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This study introduces standard Cliffordian Kaehler analogue of Hamiltonian mechanic systems. In the end, the some results related to standard Cliffordian Kaehler dynamical systems are also discussed.
This paper presents Hamilton dynamics on Clifford Kaeler manifolds. In the end, the some results related to Clifford Kaehler dynamical systems are also discussed.
This study presents standard Cliffordian Kaehler analogue of Lagrangian mechanics. Also, the some geometric and physical results related to the standard Cliffordian Kaehler dynamical systems are given.
We formulate Dirac-Kaehler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kaehler action requires to choose the lattice structure having both orientabilities on a link. The Kogut-Susskind fermion and the staggered fermion actions are derived directly from the Dirac-Kaehler fermion formulated by the Clifford product. The lattice QCD action with Dirac-Kaehler matter fermion is also derived via an inner product defined by the Clifford product.
The aim of this study is to introduce quaterinon Kaehler analogue of Lagrangian mechanics. Finally, the geometric and physical results related to quaternion Kaehler dynamical systems are also presented.
In the present paper, we introduce para-quaternionic Kaehler analogue of Lagrangian and Hamiltonian mechanical systems. Finally, the geometrical-physical results related to para-quaternionic Kaehler mechanical systems are also given.
In this study, it is introduced paracomplex analogue of Lagrangians and Hamiltonians with constraints in the framework of para-Kaehlerian manifolds. The geometrical and mechanical results on the constrained mechanical system have also been discussed.
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kahler 2-form. We compare the geometric quantization framework with several deformation quantization approaches. We find that the balanced metrics appear naturally as a result of setting the vacuum energy to be the constant function on the moduli space of semiclassical vacua. In the classical limit these metrics become Kahler-Einstein (when M a…
We derive the quantization of action, particle number, and electric charge in a Lagrangian spin bundle over M equivalent M_# union D_J, Penrose's conformal compactification of Minkowsky space, with the world tubes of massive particles removed.
Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a ``free'' fermion within the geometrical setup of spontaneously broken Yang-Mills-Higgs gauge theories. The geometrical frame discussed here gives rise to a natural class of Lagrangian densities. It is shown that the geometry of the Clifford module bundle representing a free fermion is described by a canonical spectral invariant …
The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations
本文阐明了几何热力学与基于Fisher矩阵的信息几何之间的关系，首次在热力学变量的宏观接触流形上引入Kähler度量，并通过CV流形上的精确配分函数积分和Killing矩映射的非线性Casimir函数，推广了Souriau热力学，类比于铁磁自发磁化。
In this paper we provide using the Clifford and spin-Clifford formalism and some few results of the extensor calculus a derivation of the conservation laws that follow directly from the Dirac-Hestenes equation (DHE) describing a Dirac-Hestenes spinor field (DHSF) in interaction with an external electromagnetic field without using the Lagrangian formalism. In particular, we show that the energy-momentum and total angular momentum extensors of a DHSF is not conserved in spacetime regions permitting the existence of a null electromagnetic field F but a non null electromagnetic potential A. These …
We compute the ring structure of Floer cohomology groups of Lagrangian torus fibers in some toric Fano manifolds continuing the study of \cite{CO}. Related $\AI$-formulas hold for transversal choice of chains. Two different computations are provided: a direct calculation using the classification of holomorphic discs by Oh and the author in \cite{CO}, and another method by using an {\it analogue of divisor equation} in Gromov-Witten invariants to thecase of discs. Floer cohomology rings are shown to be isomorphic to Clifford algebras, whose quadratic forms are given by the Hessians of functions…
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