论文标题
量子力学和现场理论中的交叉数字
Intersection Numbers in Quantum Mechanics and Field Theory
论文作者
论文摘要
By elaborating on the recent progress made in the area of Feynman integrals, we apply the intersection theory for twisted de Rham cohomologies to simple integrals involving orthogonal polynomials, matrix elements of operators in Quantum Mechanics and Green's functions in Field Theory, showing that the algebraic identities they obey are related to the decomposition of twisted cocycles within cohomology groups, and which, therefore,可以通过相交数来得出。我们的调查表明，一种代数方法通常适用于研究概率分布的高阶力矩，其中共同体学组的维度与独立矩的数量相对应。扭曲的共生的交点数可用于得出它们之间的线性和二次关系。我们的研究提供了物理，几何和统计数据之间相互作用的其他证据。
By elaborating on the recent progress made in the area of Feynman integrals, we apply the intersection theory for twisted de Rham cohomologies to simple integrals involving orthogonal polynomials, matrix elements of operators in Quantum Mechanics and Green's functions in Field Theory, showing that the algebraic identities they obey are related to the decomposition of twisted cocycles within cohomology groups, and which, therefore, can be derived by means of intersection numbers. Our investigation suggests an algebraic approach generically applicable to the study of higher-order moments of probability distributions, where the dimension of the cohomology groups corresponds to the number of independent moments; the intersection numbers for twisted cocycles can be used to derive linear and quadratic relations among them. Our study offers additional evidence of the intertwinement between physics, geometry, and statistics.
