Related papers: Problems and Solutions in a Graduate Course in Cla…
Instead of a linear system of equations for a free electromagnetic field, we propose a nonlinear system of equations. The classical electrodynamics is preseved. The appeared solutions (the electromagnetic fields) having photon properties.…
We discuss the mapping of the conservative part of two-body electrodynamics onto that of a test charged particle moving in some external electromagnetic field, taking into account recoil effects and relativistic corrections up to second…
Introductory algebra-based physics courses frequently feature multiple student major populations in the same course section, however, different majors' requirements may impact students' motivations towards different aspects of the course…
We consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
We obtain classical solutions of $\l$-deformed $\s$-models based on $SL(2,\mathbb{R})/U(1)$ and $SU(2)/U(1)$ coset manifolds. Using two different sets of coordinates, we derive two distinct classes of solutions. The first class is expressed…
This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and…
Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be…
We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of…
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
There are two fundamental problems studied by the theory of hamiltonian integrable systems: integration of equations of motion, and construction of action-angle variables. The third problem, however, should be added to the list: separation…
We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…
Short time existence of classical solutions is proved for a system of equations that involves a three excitations kinetic operator. The system is related to the description of a gas of bosons below but close to the critical temperature,…
The present tutorial aims at covering the fundamentals of electromagnetism, in a condensed and clear manner. Some solved and proposed exercises have been included. The reader is assumed to have knowledge of basic electricity, partial…
We derive the semiclassical series for the partition function of a one-dimensional quantum-mechanical system consisting of a particle in a single-well potential. We do this by applying the method of steepest descent to the path-integral…
Despite the many successes of the relativistic quantum theory developed by Horwitz, et. al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination…
We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked…
We describe how graduate students categorize introductory mechanics problems based on the similarity of their solutions. Graduate students were asked at the end of a teaching assistant training class to categorize problems from their own…