Necessity of Integral Formalism

• 作者: 陶勇
• 来源期刊: 理论物理通讯：英文版
• 学科: 数学
• 关键词: 形式主义 积分算子 Berry相 动力学方程 量子绝热定理 绝热极限 物理学 波函数
• 年，卷（期）: 2011,（10）
• 页码范围: 648-654
• 页数: 7页
• 分类号: O177.6|O431
• 语种: 英文

摘要

To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 （1974） 44fi], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 （1975） 3846]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 （2004） 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schroedinger differential equation （i.e., differential formalism for wave function） shall lead to vanishing Berry phase and that the Schroedinger integral equation （i.e., integral formalism for wave function）, in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion： There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	陶勇		4	2	1.0	1.0