De Donder Weyl: someone give an example question?

This requires knowledge of the De Donder-Weyl equations and the appropriate boundary conditions for the system.
  • #1
berra
21
0

Homework Statement


Could someone give an example question in De Donder-Weyl theory (the multisymplectic theory where the hamiltonian is not parametrized by time, it's on wikipedia).

Homework Equations


The relevant equations should not be too complicated, just complicated enough to use the multisymplectic approach.

The Attempt at a Solution


I have read lots of articles on arxiv but do not understand enough of the concepts (some things look similar to clifford algebra and clifford calculus, like the orthogonality stuff). It would be very educational with an example.

Please don't attack me for using the template for requesting a question, I did fill in all the headings.
 
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  • #2
One example question could be:Given a system of differential equations, evaluate the multisymplectic form associated with the system and determine whether it is conserved.
 

Related to De Donder Weyl: someone give an example question?

1. What is De Donder Weyl theory?

De Donder Weyl theory, also known as covariant Hamiltonian formalism, is a mathematical framework used to describe physical systems in terms of their coordinates, momenta, and time evolution. It is a generalization of Hamiltonian mechanics that takes into account the principles of relativity and gauge invariance.

2. How does De Donder Weyl theory differ from traditional Hamiltonian mechanics?

Unlike traditional Hamiltonian mechanics, which is based on the concept of phase space, De Donder Weyl theory uses a mathematical structure called a multisymplectic space to describe the dynamics of a physical system. This allows for a more comprehensive and covariant treatment of systems that are subject to gauge transformations.

3. Can you give an example of a physical system that can be described using De Donder Weyl theory?

An example of a physical system that can be described using De Donder Weyl theory is a charged particle moving in an electromagnetic field. The theory allows for a covariant description of the particle's dynamics, taking into account the gauge invariance of the electromagnetic field.

4. How does De Donder Weyl theory relate to other theories in physics?

De Donder Weyl theory is closely related to other mathematical frameworks used in physics, such as Lagrangian and Hamiltonian mechanics, as well as the theory of general relativity. It can also be used to derive and unify other physical theories, such as classical field theory and quantum field theory.

5. Are there any practical applications of De Donder Weyl theory?

De Donder Weyl theory has found applications in various fields, including classical mechanics, electromagnetism, and general relativity. It has also been used in the study of geometric quantization and the development of new mathematical tools for analyzing and solving physical problems.

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