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        "quote": "要得到伪经典力学，把Grassmann代数 $\\Lambda^*(\\mathbb R^n)$ 视为经典可观测量的代数，也就是“费米子”相空间 $V=\\mathbb R^n$ 上的函数代数。费米子相空间不必是偶数维的。在这个代数上可以定义合适的[<u class=\"concept-term\" data-concept-reference=\"concepts/mechanics/fermionic-poisson-bracket\" data-concept-identity=\"urn:uuid:05c92274-bda7-4225-b24d-846ec64b2dbc\" data-concept-route=\"/concept-identities#concept-05c92274-bda7-4225-b24d-846ec64b2dbc\" id=\"first-81dcf2b2a80924f1fd88-zh\">费米子泊松括号(fermionic Poisson bracket)</u>](../../../../../concepts/mechanics/fermionic-poisson-bracket)。通常的泊松括号在线性函数上是反对称双线性形式 $\\Omega(\\cdot,\\cdot)$；费米子泊松括号则以线性函数上的对称双线性形式，即内积 $(\\cdot,\\cdot)$ 为基础。",
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        "quote": "To get pseudo-classical mechanics, we think of the Grassmann algebra $\\Lambda ^ { * } ( \\mathbf { R } ^ { n } )$ as our algebra of classical observables, an algebra we can think of as functions on a “fermionic” phase space $V = \\mathbf { R } ^ { n }$ (note that in the fermionic case, the phase space does not need to be even dimensional). We want to find an appropriate notion of [<u class=\"concept-term\" data-concept-reference=\"concepts/mechanics/fermionic-poisson-bracket\" data-concept-identity=\"urn:uuid:05c92274-bda7-4225-b24d-846ec64b2dbc\" data-concept-route=\"/concept-identities#concept-05c92274-bda7-4225-b24d-846ec64b2dbc\" id=\"first-81dcf2b2a80924f1fd88-en\">fermionic Poisson bracket</u>](../../../../../concepts/mechanics/fermionic-poisson-bracket) operation on this algebra, and it turns out that this can be done. While the standard Poisson bracket is an antisymmetric bilinear form $\\Omega ( \\cdot , \\cdot )$ on linear functions, the fermionic Poisson bracket will be based on a choice of symmetric bilinear form on linear functions, equivalently, a notion of inner product $( \\cdot , \\cdot )$",
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