Hamiltonian diagonalization in hybrid quantum cosmology

Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology

In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly in the framework of loop quantum cosmology. We investigate the phenomenological implications of this model in the semi-classical regime an...

Exact Diagonalization Of The Fractional Quantum Hall Many-Body Hamiltonian In The Lowest Landau Level

For a gaussian interaction V (x, y) = λ e− x2+y2 2r2 with long range r >> lB, lB the magnetic length, we rigorously prove that the eigenvalues of the finite volume Hamiltonian HN,LL = PLLHNPLL, HN = ∑N i=1 ( −i~∇xi − eA(xi) 2 + ∑ i,j; i6=j V (xi − xj), rotA = (0, 0, B), and PLL the projection onto the lowest Landau level, are given by the following set: Let M be the number of flux quanta flowin...

Quantum Hamiltonian diagonalization and Equations of Motion with Berry Phase Corrections

Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum sys...

Diagonalization of the Hamiltonian in a Chromomagnetic Field

We demonstrate how to find both the color diagonal form of the squared Dirac equation in the axial color background and the transformation of the color space, which makes this equation diagonal.