A survey on geometric frameworks for action-dependent classical field theories and their relationship

2025/06/13 by Jordi Gaset-Rifà, Gaset-Rifà, Jordi, Xavier Rivas +3 · 2 citations
Computer Science · Engineering · #35Q99 #35R01 #53C15 #53D10 #53Z05 #58A10 #70G45 #70S05 #70S10 #Advanced Vision and Imaging #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.2506.11646

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

This work presents a comprehensive overview of three recently developed geometric frameworks for the study of classical action-dependent field theories. Specifically, the three underlying geometric structures - namely, k-contact, k-cocontact, and multicontact - are first introduced, and then used to develop the Lagrangian and Hamiltonian formalisms of the aforementioned theories. Finally, the relationship among these three types of structures is analyzed in the case of trivial bundles; as well as the comparison with other alternative definitions of multicontact structure presented in the literature.

Citations

• Symmetries and Noether's theorem for multicontact field theories
• Time-dependent contact mechanics
• Contact foliations and generalised Weinstein conjectures
• An invitation to multisymplectic geometry
• Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory

Cited by

• Skinner--Rusk formalism of action-dependent multicontact field theories
• From variational principles to geometry

Related

• Geometric Structures in Field Theory
• Skinner--Rusk formalism of action-dependent multicontact field theories
• Symmetries and Noether's theorem for multicontact field theories
• Geometrical aspects of contact mechanical systems and field theories
• Superanalogs of symplectic and contact geometry and their applications to quantum field theory