p-Adic和Adelic空间上二次Lagrangian的路径积分
Path Integrals for Quadratic Lagrangians on p-Adic and Adelic Spaces
摘要：
考虑了普通、p-adic和adelic量子力学中的费曼路径积分。对二维二次拉格朗日系统的相应概率幅$ K(x^{"},t^{"};x',t')$进行了解析计算，并将所得表达式推广到任何有限维空间.这些通式以数域${\mathbb R} \leftrightarrow {\mathbb Q}_p$和${\mathbb Q}_p \leftrightarrow {\mathbb Q}_{p'} \, ,\, p\neq p'$互换时不变的形式给出。根据这一不变性，我们知道，在量子现象的数学物理中，最大路径积分是一个基本的对象。
英文摘要：
Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically and obtained expressions are generalized to any finite-dimensional spaces. These general formulas are presented in the form which is invariant under interchange of the number fields ${\mathbb R} \leftrightarrow {\mathbb Q}_p$ and ${\mathbb Q}_p \leftrightarrow {\mathbb Q}_{p'} \, ,\, p\neq p'$. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum phenomena.
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