Hamiltonian reduction and quantization on symplectic manifolds.
Higher symmetries of the Laplacian via quantization
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined...
Infinite-dimensional Lie groups and algebras in mathematical physics.
Lagrangian and hamiltonian aspects of Josephson type media
Locally variational invariant field equations and global currents: Chern-Simons theories
We introduce the concept of conserved current variationally associated with locally variational invariant field equations. The invariance of the variation of the corresponding local presentation is a sufficient condition for the current beeing variationally equivalent to a global one. The case of a Chern-Simons theory is worked out and a global current is variationally associated with a Chern-Simons local Lagrangian.
Multi-time sprays and -traceless maps on .
Multivector fields and connections. Applications to field theories.
Se estudia la integrabilidad de campos multivectoriales en variedades diferenciables y la relación entre algunos tipos de campos multivectoriales en un fibrado de jets y conexiones en dicho fibrado. Como caso particular se relacionan los campos multivectoriales integrables y las conexiones cuyas secciones integrales son holonómicas. Como aplicación de todo ello, estos resultados permiten escribir las ecuaciones de campo de las teorías clásicas de campos de primer orden en varias formas equivalentes....
Noether’s theorem for a fixed region
We give an elementary proof of Noether's first Theorem while stressing the magical fact that the global quasi-symmetry only needs to hold for one fixed integration region. We provide sufficient conditions for gauging a global quasi-symmetry.
Numerical solution of differential-algebraic equations for constrained mechanical motion.
On a Differential Equation with Left and Right Fractional Derivatives
Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05We treat the fractional order differential equation that contains the left and right Riemann-Liouville fractional derivatives. Such equations arise as the Euler-Lagrange equation in variational principles with fractional derivatives. We reduce the problem to a Fredholm integral equation and construct a solution in the space of continuous functions. Two competing approaches in formulating differential equations of fractional order...
On higher order geometry on anchored vector bundles
Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
On planar selfdual electroweak vortices
On the nature of time.
Optique Géométrique et invariance de jauge : Solutions oscillantes d’amplitude critique pour les équations de Yang-Mills
Particles in the superworldline and BRST
In this short note we discuss -supersymmetric worldlines of relativistic massless particles and review the known result that physical spin- fields are in the first BRST cohomology group. For , emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background.
Permutations; isotropy and smooth cyclic group actions on definite 4-manifolds.
Quantum information from graviton-matter gas.
Radiation reaction, renormalization and Poincaré symmetry.
Schwinger-Fronsdal theory of abelian tensor gauge fields.
Second variational derivative of local variational problems and conservation laws
We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that...