We apply the singular gauge transformation to the constraint equation for the lowest Landau level to investigate the generic properties of the quasiparticles of the fractional quantum Hall system by using the collective-field-theory approach. It shows a transparent connection with Laughlin s wave functions. If we take an average over the wave functional for the constraint equation, the resultin...

background when a primary radiation interacts with a medium, the secondary radiations are produced, that the contribution of these secondary radiation should considered in the calculation of dose. build-up factor is a dosimetric correction factor to assume effect of secondary radiation in calculation of dose. calculation of this factor is very difficult and time consuming. due to significance o...

Consider a Riemannian spin manifold of dimension n ≥ 3 and denote by D the Dirac operator acting on spinor fields. A solution of the Einstein-Dirac equation is a spinor field ψ solving the equations Ric − 1 2 S · g = ± 1 4 T ψ , D(ψ) = λψ. Here S denotes the scalar curvature of the space, λ is a real constant and T ψ is the energy-momentum tensor of the spinor field ψ defined by the formula

Class Meeting # 24: Transport Equations and Burger’s Equation In these notes, we introduce a class of evolution PDEs known as transport equations. Such equations arise in a physical context whenever a quantity is “transported” in a certain direction. Some important physical examples include the mass density flow for an incompressible fluid, and the Boltzmann equation of kinetic theory. We discu...

The freedom in choosing finite renormalizations in quantum field theories (QFT) is characterized by a set of parameters {ci}, i = 1 . . . , n . . ., which specify the renormalization prescriptions used for the calculation of physical quantities. For the sake of simplicity, the case of a single c is selected and chosen mass-independent if masslessness is not realized, this with the aim of expres...

We investigate the use of edge element basis vectors in an integral equation solution for three-dimensional geophysical electromagnetic modelling. Expansion of the total electric field within the region of anomalous conductivity in terms of these basis vectors gives a bilinear variation of each component of the field within a cell in the two directions perpendicular to the component (and so a d...