• Corpus ID: 119137777

Classical field theories from Hamiltonian constraint: Symmetries and conservation laws

@article{Zatloukal2016ClassicalFT,
  title={Classical field theories from Hamiltonian constraint: Symmetries and conservation laws},
  author={V{\'a}clav Zatloukal},
  journal={arXiv: Mathematical Physics},
  year={2016}
}

• V. Zatloukal
• Published 13 April 2016
• Mathematics
• arXiv: Mathematical Physics

We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a generalized multivector-valued momentum is introduced. We derive a field-theoretic Hamiltonian version of the Noether theorem, and identify generalized Noether currents with the momentum contracted with symmetry-generating vector fields. Their relation to the traditional vectorial Noether currents is then established. Throughout, we employ the mathematical language of geometric algebra and calculus.