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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...
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...
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...
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...
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...
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...
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.
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.The scalar field obeys Dirichlet boundary conditions at the perimeter of the polygon.
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.
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 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...
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...

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