标题： 在类似Liouville量子引力作用下的足球比赛中最优进球得分 显示英文标题

标题： Scoring a Goal optimally in a Soccer game under Liouville-like quantum gravity action

摘要： 在本文中，我们提出了一种新的理论模型，通过使用费曼路径积分方法，在存在随机进球动态的情况下，找出与足球运动员相关的最优权重，其中球员的行动是在$\sqrt{8/3}$-Liouville 量子引力表面上进行的。 在确定最优权重之前，我们首先建立了一个无穷逻辑，该逻辑可以处理策略空间上的无限变量，然后开发了这种逻辑的量子公式，最后，基于此，我们能够证明该游戏的Lefschetz-Hopf不动点的存在性。 如同在竞争性比赛中，所有可能的标准得分策略都为对方球队所知，球员的行为具有随机性，并且他们可能会有一些比较优势来得分。 此外，在确定最优权重的过程中，考虑了诸如由于下雨带来的不确定性、球员的控球和传球技能、比赛是白天比赛还是昼夜交替比赛、拥有主场观众的优势以及行动配置的信息不对称等条件。 显示英文摘要

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.