Covariant classical field theory


Covariant classical field theory

In recent years, there has been renewed interest in covariant classical field theory. Here, classical fields are represented by sections of fiber bundles and their dynamics is phrased in the context of a finite-dimensional space of fields. Nowadays, it is well known that jet bundles and the variational bicomplex are the correct domain for such a description. The Hamiltonian variant of covariant classical field theory is the covariant Hamiltonian field theory where momenta correspond to derivatives of field variables with respect to all world coordinates. Non-autonomous mechanics is formulated as covariant classical field theory on fiber bundles over the time axis \mathbb R.

Derivation and proof

The worksheet provides some of the geometric structure to the covariant formalism of first-order classical field theories. Talk:Covariant classical field theory/workpage

See also

References


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Covariant Hamiltonian field theory — Applied to classical field theory, the familiar symplectic Hamiltonian formalism takes the form of instantaneous Hamiltonian formalism on an infinite dimensional phase space, where canonical coordinates are field functions at some instant of time …   Wikipedia

  • Classical field theory — A classical field theory is a physical theory that describes the study of how one or more physical fields interact with matter. The word classical is used in contrast to those field theories that incorporate quantum mechanics (quantum field… …   Wikipedia

  • Scalar field theory — In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a scalar , in contrast to a vector or tensor field. The quanta of the… …   Wikipedia

  • Field (physics) — The magnitude of an electric field surrounding two equally charged (repelling) particles. Brighter areas have a greater magnitude. The direction of the field is not visible …   Wikipedia

  • Field equation — A field equation is an equation in a physical theory that describes how a fundamental force (or a combination of such forces) interacts with matter. The four fundamental forces are the gravitational force, the electromagnetic force, the strong… …   Wikipedia

  • Classical electromagnetism and special relativity — This article is about the contribution of special relativity to the modern theory of classical electromagnetism. For the contribution of classical electromagnetism to the development of special relativity, see History of special relativity. For a …   Wikipedia

  • Covariant formulation of classical electromagnetism — Electromagnetism Electricity · …   Wikipedia

  • Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… …   Wikipedia

  • Classical unified field theories — Since the 19th century, some physicists have attempted to develop a single theoretical framework that can account for the fundamental forces of nature – a unified field theory. Classical unified field theories are attempts to create a unified… …   Wikipedia

  • Classical theories of gravitation — The current Gold Standard Theory of Gravitation is the general theory of relativity. This is a classical, relativistic field theory (physics) of gravitation. At present, there is no quantum theory of gravitation. Contents 1 Discussion 2 See also …   Wikipedia