Related papers: Lecture Notes on Mathematical Methods of Classical…
These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
This is the second paper in a series on the dynamics of matter fields in the causal set approach to quantum gravity. We start with the usual expression for the Lagrangian of a charged scalar field coupled to a SU(n) Yang-Mills field, in…
The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this…
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.
Background fields of electromagnetic and gravitational type emerge in the low kinetic energy limit of any regular Lagrangian system and, in particular, in the corresponding limit of any spacetime theory in which the free motion of test…
In the present work, a consistent Lagrangian model that encapsulates fully kinetic ions and gyrokinetic electrons for solar wind electromagnetic turbulence is formulated. Using a consistent method, where both electrons and protons are…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
We study properties of classical reparametrization-invariant matter systems, mainly the relativistic particle and its d-brane generalization. The corresponding matter Lagrangian naturally contains background interaction fields, such as a…
The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…
These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black…
This article is a review of what could be considered the basic mathematics of Einstein-Cartan theory. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and Bianchi identities,…