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An introduction to circle valued Morse theory and Novikov homology, from an algebraic point of view.
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the Dirac equation is developed. Avoiding disadvantages of the standard approach in the description of exited…
The flux of angular momentum of electromagnetic field of an arbitrarily moving point charge is investigated. General equations are obtained for the transfer of angular momentum at arbitrary distance from the charge, and corresponding…
Using classical description of spin degrees of freedom, we extend recent formulation of the perfect-fluid hydrodynamics for spin-polarized fluids to the case including dissipation. Our work is based on the analysis of classical kinetic…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.
We propose a generalization of the momentum map on a symplectic manifold with a Lie algebra action to a Courant algebroid structure. The theory of a momentum section on a Lie algebroid is generalized to the theory compatible with a Courant…
A comprehensive review on Cook's contribution in the theory of NP-Completeness with relations to modern mathematics.
The most celebrated aspects of precision physics are briefly summarized. New ideas are also introduced that may lead to further developments in the field of radiative corrections, with special emphasis to multi-loop numerical evaluation and…
This paper gives a slight refinement of a theorem of Hamilton, which shows that the velocity of a Keplerian motion moves on a circle.
We provide sufficient conditions for the existence of periodic solutions of the planar perturbed double pendulum with small oscillations.
Four expressions involving sums of position and velocity coordinates bounding the total angular momentum of particle systems, and by extension of any continuous or discontinuous material systems, are derived which are tighter for any…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.
We provide a new analysis of the irreducible loop integrals first considered in a 2003 paper of Wu. Using convergence ideas from probability, we produce conditions on the regulator masses so that the integrals have well-defined limits in…
In these notes, we emphasize Theorems rather than Theories concerning turbulent fluid motion. Such theorems can be viewed as constraints on the theoretical predictions and expectations of some of the greatest scientific minds of the 20th…
Lecture notes on selected topics in the theory of gravitation.
We review recent progress in calculations of one-loop QCD amplitudes. By imposing the consistency requirements of unitarity and correct behavior as the momenta of two legs become collinear, we construct ansatze for one-loop amplitudes with…
This is a comment on Chen et al Letter PRL,100, 232002 (2008).
Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…