类Liouville量子引力作用下足球比赛的最优进球
Scoring a Goal optimally in a Soccer game under Liouville-like quantum gravity action
摘要：
本文提出了一个新的理论模型，利用Feynman路径积分方法，在随机目标动力学存在的情况下，求解足球运动员的最优权值，其中运动员的作用在$\sqrt{8/3}$ -Liouville量子引力曲面上.在确定最优权重之前，我们首先建立了一个可以处理策略空间上无穷多个变量的无穷大逻辑，然后给出了这个逻辑的量子公式，最后在此基础上证明了这个博弈的Lefschetz-Hopf不动点的存在性。就像在一场竞技比赛中，对手知道所有可能的标准进球策略，球员的行为本质上是随机的，他们在进球方面会有一些比较优势。此外，由于下雨，运球和传球技术的球员，无论是白天比赛或昼夜比赛，有主场观众和行动配置文件的不对称信息的优势等条件的不确定性已被考虑的方式，以确定最佳的权重。
英文摘要：
In this paper we present a new theoretical model to find out an optimal weight associated with a soccer player under the presence of a stochastic goal dynamics by using Feynman path integral method, where the action of a player is on $\sqrt{8/3}$-Liouville Quantum Gravity surface. Before determine the optimal weight we first establish an Infinitary logic which can deal with infinite variables on the strategy space then, a quantum formula of this logic has been developed and finally, based on this we are able show the existence of a Lefschetz-Hopf fixed point of this game. As in a competitive tournament, all possible standard strategies to score goals are known to the opposition team, a player's action is stochastic in nature and they would have some comparative advantage to score goals. Furthermore, conditions like uncertainties due to rain, dribbling and passing skill of a player, whether the match is a day match or a day-night match, advantages of having home crowd and asymmetric information of action profiles have been considered on the way to determine the optimal weight.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
