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引用次数: 0
摘要
我们定义了向量场到 De Donder-Weyl 哈密顿(一阶)场论的多折射多动量束以及奇异场论所研究的适当前多折射嵌入约束子曼形上的典型提升。这些新的典型提升用于研究规则和奇异哈密顿场论中存在的所谓自然诺特对称性,以及从诺特定理中获得的相关守恒量。作为这些概念的应用,我们深入分析了 3+1 维中的克莱因-戈登场、波利亚科夫玻色弦和爱因斯坦-卡尔坦引力;作为玻色弦分析中获得的一个外围结果,我们为著名的维拉索罗约束提供了一种新的几何解释。
Canonical lifts in multisymplectic De Donder–Weyl Hamiltonian field theories
We define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder–Weyl Hamiltonian (first-order) field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether’s theorem. The Klein–Gordon field, the Polyakov bosonic string, and Einstein–Cartan gravity in 3+1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint.
期刊介绍:
Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.