Related papers: Lecture Notes on Mathematical Methods of Classical…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
This is the first of a couple of papers in which, by exploiting the capabilities of the Hamiltonian approach to general relativity, we get a number of technical achievements that are instrumental both for a disclosure of \emph{new} results…
Applied to field theory, the familiar symplectic technique leads to instantaneous Hamiltonian formalism on an infinite-dimensional phase space. A true Hamiltonian partner of first order Lagrangian theory on fibre bundles $Y\to X$ is…
We present the Hamilton-Jakobi method for the classical mechanics with constrains in Grassmann algebra. In the frame of this method the solution for the classical system characterized by the SUSY Lagrangian is obtained.
We present the Hamilton-Jakobi method for the classical mechanics with constrains in Grassmann algebra. In the frame of this method the solution for the classical system characterized by the SUSY Lagrangian is obtained.
In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of…
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of…
Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics.…
In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
The Hamiltonian formulation of the theory of J-bundles is given both in the Hamilton--De Donder and in the Multimomentum Hamiltonian geometrical approaches. (3+3) Yang-Mills gauge theories are dealt with explicitly in order to restate them…
The paper contains a differential-geometric foundations for an attempt to formulate Lagrangian (canonical) quantum field theory on fibre bundles. In it the standard Hilbert space of quantum field theory is replace with a Hilbert bundle; the…
The goal of these lectures is to introduce readers with a basic knowledge of undergraduate physics (specifically non-relativistic quantum mechanics, special relativity, and electromagnetism) to the `current theory of everything': the…
It is shown that target space diffeomorphism invariance of a generic Lagrangian for a set of scalar fields leads to an analog of Einstein equations for the geometry of a level set of these fields.
Recent work in the literature has shown that general relativity can be formulated in terms of a jet bundle which, in local coordinates, has five entries: local coordinates on Lorentzian space-time, tetrads, connection one-forms,…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
We discuss the classical mechanics on the Grassmannian and the Disc modeled on the ideal L^(2,\infty)(H). We apply methods of geometric quantization to these systems. Their relation to a flat symplectic space is also discussed.
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…