标题： 经典场论在多 momentum 相空间中的规范结构 显示英文标题

标题： Canonical Structure of Classical Field Theory in the Polymomentum Phase Space

摘要： 研究了基于德·唐德-外尔（De Donder-Weyl, DW）理论的时空对称哈密顿形式在场论中的类比结构。在$n$维时空下，$n$组多重动量与场变量的时空导数相关联。多辛$(n+1)$形式推广了简单辛形式，并引出了一个映射，该映射在水平形式（作为动力学变量的角色）和推广的哈密顿矢量场的垂直多向量之间建立联系。在所谓的哈密顿形式的子空间上定义了分级泊松括号，并导致了 Z-分级李代数的结构，其中上述映射存在。广义泊松结构以我们称之为“高阶”右格尔斯滕哈伯代数的形式出现。 场方程和形式的运动方程用 DW 哈密顿$n$形式$H\vol$（其中$\vol$是时空体积形式，$H$是 DW 哈密顿函数）的分级泊松括号来表述。简要讨论了几何标量场、电动力学以及南布-戈托弦的一些应用，以及它与场论中标准哈密顿形式的关系。这是对我们早期简明通讯（hep-th/9312162、hep-th/9410238 和 hep-th/9511039）的详细改进版本。 显示英文摘要

摘要： Canonical structure of the space-time symmetric analogue of the Hamiltonian formalism in field theory based on the De Donder-Weyl (DW) theory is studied. In $n$ space-time dimensions the set of $n$ polymomenta is associated to the space-time derivatives of field variables. The polysymplectic $(n+1)$-form generalizes the simplectic form and gives rise to a map between horizontal forms playing the role of dynamical variables and vertical multivectors generalizing Hamiltonian vector fields. Graded Poisson bracket is defined on forms and leads to the structure of a Z-graded Lie algebra on the subspace of the so-called Hamiltonian forms for which the map above exists. A generalized Poisson structure arises in the form of what we call a ``higher-order'' and a right Gerstenhaber algebra. Field euations and the equations of motion of forms are formulated in terms of the graded Poisson bracket with the DW Hamiltonian $n$-form $H\vol$ ($\vol$ is the space-time volume form and $H$ is the DW Hamiltonian function). A few applications to scalar fields, electrodynamics and the Nambu-Goto string, and a relation to the standard Hamiltonian formalism in field theory are briefly discussed. This is a detailed and improved account of our earlier concise communications (hep-th/9312162, hep-th/9410238, and hep-th/9511039).