论文标题
减少$ l_ \ infty $ - 多链歧管上可观察物的代数
Reduction of $L_\infty$-Algebras of Observables on Multisymplectic Manifolds
论文作者
论文摘要
我们为在兼容的lie代数$ \ mathfrak {g} \ curvearrowrowrowright m $ m $和子集$ n \ subset m $的情况下，为$ l_ \ infty $ infty $ - infty $ - 代数的$ l_ \ infty $ algebra of ospervable $ algebra。这在符合性的设定中复制了Marsder-Weinstein-Meyer上可观察到的泊松代数，每当存在缩小空间时，都会减少空间，但否则与Dirac，Śniatycki-Weinstein和Arms-Cushman-Gotay-Gotay-Gotay可观察的还原计划不同。我们研究了各种示例，包括多角膜束和多相空间，并以对经典现场理论和量化的应用的讨论结论。
We develop a reduction scheme for the $L_\infty$-algebra of observables on a premultisymplectic manifold $(M,ω)$ in the presence of a compatible Lie algebra action $\mathfrak{g}\curvearrowright M$ and subset $N\subset M$. This reproduces in the symplectic setting the Poisson algebra of observables on the Marsden-Weinstein-Meyer symplectic reduced space, whenever the reduced space exists, but is otherwise distinct from the Dirac, Śniatycki-Weinstein, and Arms-Cushman-Gotay observable reduction schemes. We examine various examples, including multicotangent bundles and multiphase spaces, and we conclude with a discussion of applications to classical field theories and quantization.
