标题： 场论的拉格朗日-哈密顿统一形式体系 显示英文标题

标题： Lagrangian-Hamiltonian unified formalism for field theory

摘要： 鲁斯-斯金纳形式主义的发展是为了给出一个几何化的统一形式化方法，用于描述机械系统。它包含了拉格朗日和哈密顿描述这些系统的全部特征（包括动力学方程和解、约束、勒让德映射、演化算子、等价性等）。在这项工作中，我们将这一统一框架扩展到一阶经典场论，并展示了这种描述如何涵盖了拉格朗日和哈密顿形式主义的主要特征，适用于正则和奇异情况。这一表述是朝着偏微分方程最优控制理论进一步应用迈出的第一步。 显示英文摘要

摘要： The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for PDE's.