Path integrals for quadratic lagrangians on p-adic and adelic spaces
Path integrals for quadratic lagrangians on p-adic and adelic spaces
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p-adic 和adelic 空间上二次拉格朗日的路径积分
DOI：
10.1134/s2070046610040060
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Z. Rakic
中科院分区：
文献类型：
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作者：
B. Dragovich;Z. Rakic
讨论了普通量子力学、p进量子力学和adelic量子力学中的Feynman路径积分。对具有二次拉格朗日的二维系统的相应概率幅值K(x“，t”；x‘，t’)进行了解析计算，并将所得表达式推广到任意有限维空间。这些一般公式的形式在数域ℝ↔ℚp和ℚ↔ℚp，p≠p‘的互换下是不变的。根据这一不变性，我们得出结论：在量子现象的数学物理中，路径积分是一个基本的对象。
Feynman’s path integrals in ordinary,p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudesK(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 ℝ ↔ ℚpand ℚ ↔ ℚp,p≠p′. According to this invariance we have that adelic path integral is a fundamental object in mathematical physics of quantum phenomena.