116 research outputs found
Hodge duality operators on left covariant exterior algebras over two and three dimensional quantum spheres
No full textpeer reviewedUsing non-canonical braidings, we first introduce a notion of symmetric tensors and corresponding Hodge operators on a class of left-covariant 3d differential calculi over SUq(2), then we induce Hodge operators on the left-covariant 2d exterior algebra over the Podle`s quantum sphere
Calculi, Hodge operators and Laplacians on a quantum Hopf fibration
No full text We describe Laplacian operators on the quantum group SUq(2) equipped with the four-dimensional bicovariant differential calculus of Woronowicz as well as on the quantum homogeneous space [Formula: see text] with the restricted left covariant three-dimensional differential calculus. This is done by giving a family of Hodge dualities on both the exterior algebras of SUq(2) and [Formula: see text]. We also study gauged Laplacian operators acting on sections of line bundles over the quantum sphere. </jats:p
Linear algebra and analytic geometry for physical sciences
No full textA self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number. The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification
Dirac operators on the S3 and S2 spheres
No full text We describe both the Hodge–de Rham and the spin manifold Dirac operator on the spheres [Formula: see text] and [Formula: see text], following the formalism introduced by Kähler, and exhibit a complete spectral resolution for them in terms of suitably globally defined eigenspinors. </jats:p
I principi della meccanica delineati in una nuova forma
No full textQuest’opera presenta la traduzione in italiano della prima edizione di "Die
Prinzipien der Mechanik in neuem Zusammenhange dargestellt", il manuale a cui
Hertz lavorò negli ultimi anni della sua vita come professore all’Università di Bonn
e che fu pubblicato, poco dopo la sua scomparsa, nel 1895 a cura del suo allievo
Philipp von Lenard; e contiene la traduzione sia della prefazione preparata dallo
stesso Hertz sia di quella, ammirata e commossa, scritta da Hermann von
Helmholtz, che fu di Hertz maestro e mentore. Essa si avvale di una prefazione originale di Asim O. Barut, che sottolinea quanto le linee di ricerca più moderne abbiano fatto propria l’impostazione di Hertz di sviluppare una formulazione unificata dei fenomeni meccanici ed elettromagnetici in natura
- …
