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arXiv · 2409.08340

Practical Introduction to Action-Dependent Field Theories

Manuel de León·Jordi Gaset Rifà·Miguel C. Muñoz-Lecanda·Xavier Rivas·Narciso Román-Roy
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Abstract

Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a well-defined notion of symmetries and a Noether theorem. This makes them especially suited for open systems. After a conceptual introduction, we make a quick presentation of a new mathematical framework for action-dependent field theory: multicontact geometry. The formalism is illustrated with a variety of action-dependent Lagrangians, some of which are regular and others singular, derived from well-known theories whose Lagrangians have been modified to incorporate action-dependent terms. Detailed computations are provided, including the constraint algorithm for the singular cases, in both the Lagrangian and Hamiltonian formalisms. These are the one-dimensional wave equation, the Klein-Gordon equation and the telegrapher equation, Maxwell's electromagnetism, Metric-affine gravity, the heat equation and Burguers' equation, the Bosonic string theory, and (2+1)-dimensional gravity and Chern-Simons equation.

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Manuel de León, Jordi Gaset Rifà, Miguel C. Muñoz-Lecanda, Xavier Rivas, Narciso Román-Roy. 2025-04-04. Practical Introduction to Action-Dependent Field Theories. https://doi.org/10.1002/prop.70000

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