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本文计算了秩为n+1的一类特殊的Verlinde模性范畴l的Casimir数,计算结果表明该Casimir数为2n+4.作为应用,由Higman定理知域K上的Grothendieck代数Gr (l)⊗Z K是半单代数当且仅当2n+4在域K中不为零.这也给出了第二类型n+1次Dickson多项式En+1(X)在K[X]中无重因式的一个等价刻画.如果2n+4在域K中为零,借助于Dickso...
CASIMIR OPERATORS AND MONODROMY REPRESENTATIONS OF GENERALISED BRAID GROUPS
CASIMIR OPERATORS MONODROMY REPRESENTATIONS GENERALISED BRAID GROUPS
2015/10/14
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W . We construct a one parameter family of flat connections ∇κ on h with values in any finite–dimensional g–moduleV...
Van der Waals-Casimir-Polder interaction of an atom with a composite surface
Van der Waals-Casimir-Polder interaction atom composite surface Atomic Physics
2012/5/29
We study the dispersion interaction of the van der Waals and Casimir-Polder (vdW-CP) type between a neutral atom and the surface of a metal by allowing for nonlocal electrodynamics, i.e. electron diff...
Singular Casimir Elements of the Euler Equation and Equilibrium Points
Singular Casimir Elements Euler Equation Equilibrium Points Analysis of PDEs
2011/10/10
Abstract: The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal...
Singular Casimir Elements of the Euler Equation and Equilibrium Points
the Euler Equation Equilibrium Points Analysis of PDEs
2011/9/21
Abstract: The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal...
Topological Casimir effect in compactified cosmic string spacetime
Topological Casimir effect compactified cosmic string spacetime
2011/10/18
We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling in the generalized co...
Temperature (in)dependence of the Casimir-Polder potential of a particle near a metallic sphere
Casimir-Polder potential particle metallic sphere Temperature independence
2011/8/16
Abstract: It has recently been shown that the Casimir-Polder potential of a particle in an energy eigenstate near a conducting body can be virtually temperature independent, provided the separation be...
Gedanken experiments with Casimir forces, vacuum energy, and gravity
Casimir force quantum vacuum gravity mass
2011/8/2
Gedanken experiments with Casimir forces, vacuum energy, and gravity.
We prove a certain unexpected regularity of geodesic restrictions for the (hyperbolic) Casimir operator. We prove a nontrivial bound on L2-norm of a geodesic restriction for eigenfunctions
of the Cas...
We study the Casimir energy of a scalar field for a regular polygon with N sides.
Casimir energy scalar field regular polygon
2011/2/25
We study the Casimir energy of a scalar field for a regular polygon with N sides.The scalar field obeys Dirichlet boundary conditions at the perimeter of the polygon.
Modal Hamiltonian interpretation of quantum mechanics and Casimir operators: the road towards quantum field theory
Modal Hamiltonian interpretation of quantum mechanics Casimir operators quantum field theory
2011/3/2
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields.
A Dispersion Relation for the Density of States With Application to the Casimir Effect
Dispersion Relation the Density of States the Casimir Effect
2010/12/27
The trace of a function of a Schrodinger operator minus the same for the Laplacian can be expressed in terms of the determinant of its scattering matrix. The naive formula for this determinant is dive...
We study the zero point energy of massless scalar and vector fields subject to spheroidal boundary conditions. For massless scalar fields and small ellipticity the zero-point energy can be found usin...
Finite Casimir Energies of Intersecting Objects
Finite Casimir Energies Intersecting Objects
2010/12/27
Finite Casimir energies for bosonic fields interacting locally with $N$ objects that do not all have a common intersection are defined by geometrical subtractions. The perturbative expansion for $\be...
A consequence of the repulsive Casimir-Lifshitz force on nano-scale and the related Wheeler propagator in the classical electrodynamics
repulsive Casimir-Lifshitz force nano-scale related Wheeler propagator
2010/12/24
Mainly on nano-scale, but maybe not exclusively, it can be imagined a spontaneous charge disjunction inside certain media due to the fluctuations, collisions, wall effects, radiation or/and other pre...