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

TL;DR

This paper introduces a novel theoretical model using Liouville Quantum Gravity and Feynman path integrals to determine the optimal strategy weight for scoring goals in soccer, accounting for various uncertainties and strategic factors.

Contribution

It develops a new quantum logical framework and proves the existence of a fixed point for the game, integrating complex physical and strategic considerations.

Findings

Existence of a Lefschetz-Hopf fixed point in the game model

Incorporation of stochastic goal dynamics and environmental uncertainties

Development of a quantum logical approach to strategic decision-making

Abstract

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.