Action principle and the Hamiltonian formulation for the Maxwell–Vlasov equations on a symplectic leaf

1994 ◽  
Vol 1 (8) ◽  
pp. 2409-2418 ◽  
Author(s):  
Tor Flå
Keyword(s):  
Hamiltonian Formulation ◽  
Action Principle ◽  
Vlasov Equations ◽  
Symplectic Leaf

Hamiltonian Formulation and Action Principle for the Lorentz-Dirac System

2006 ◽  
Vol 45 (6) ◽  
pp. 1091-1106 ◽  
Author(s):  
V. G. Kupriyanov
Keyword(s):  
Hamiltonian Formulation ◽  
Action Principle ◽  
Dirac System

A new classical theory of electrons. II

1952 ◽  
Vol 212 (1110) ◽  
pp. 330-339 ◽  
Keyword(s):  
Classical Theory ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Present Theory ◽  
Action Principle ◽  
Electron Stream ◽  
General Action

An analysis is made of the motion of a stream of electrons obeying Lorentz’s equations of motion. It leads to a more general action principle than that of an earlier paper, containing two new field variables. The present theory allows vorticity in the electron stream, while still involving e and m only in the ratio e/m . A Hamiltonian formulation of the equations is deduced.

A reformulation of the Born-Infeld electrodynamics

1960 ◽  
Vol 257 (1288) ◽  
pp. 32-43 ◽  
Keyword(s):  
Point Charge ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Charged Particles ◽  
Dynamical Theory ◽  
Action Principle ◽  
Field Equations ◽  
Maxwell Electrodynamics ◽  
Recent Developments ◽  
Theory Of Fields

The electrodynamics proposed by Born & Infeld in 1934 differs from the Maxwell electrodynamics for very strong fields and gives a finite total energy for the field around a point charge. At that time not much was known about the dynamical theory of fields, and recent developments of this subject enable one to give a better formulation of the Born-Infeld theory. The basis is a comprehensive action principle that determines both the field equations and the equations of motion of charged particles. From this action principle a Hamiltonian formulation is obtained, the various Hamiltonian constraints being worked out. The classical theory is found to be completely satisfactory, but difficulties arise with the passage to the quantum theory, which appear to be insoluble with present methods of quantization.

VARIATIONAL OPTIMUM ACTION PRINCIPLE

2019 ◽  
Vol 7 (67) ◽  
Author(s):  
V. V. Nikitin
Keyword(s):  
Action Principle

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

scholarly journals Currents, charges and algebras in exceptional generalised geometry

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
David Osten
Keyword(s):  
Current Algebra ◽  
Hamiltonian Formulation ◽  
Building Blocks ◽  
Lie Derivative ◽  
Consistency Check ◽  
World Volume ◽  
Invariant Currents ◽  
Invariant Current ◽  
M Theory ◽  
A Current

Abstract A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the Ed(d) generalised Lie derivative. Ed(d)-covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non- geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents.

scholarly journals Port-Hamiltonian formulation of two-phase flow models

2021 ◽  
Vol 149 ◽  
pp. 104881
Author(s):  
H. Bansal ◽  
P. Schulze ◽  
M.H. Abbasi ◽  
H. Zwart ◽  
L. Iapichino ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Hamiltonian Formulation ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Models
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