Relativistic few-body problem. I. Two-body equations
Relativistic few-body problem. I. Two-body equations
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相对论少体问题。
DOI：
10.1103/physrevc.26.2203
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发表时间：
1982
影响因子：
3.1
通讯作者：
F. Gross
中科院分区：
文献类型：
--
作者：
F. Gross
本文首先解释了两体相对论方程在其中一个质量变得非常大时应接近单体方程这一要求的含义。发现Bethe-Salpeter方程不满足这一要求。构造了一个依赖于参数$\ensuremath{-}1\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}1$的三维方程的无限族，所有这些方程都满足这个极限。当$|\ensuremath{\nu}|=1$其中一个粒子在它的质量壳层上;当$\ensuremath{\nu}=0$两个粒子都相等地离开质量壳层。研究了这个族的四阶不可约核在所有$\ensuremath{\nu}$的扩展静态极限中的性质。我们发现，无论是标量理论还是自旋半核子与矢量π介子相互作用的手征理论，静态极限中的首阶项对任何$\ensuremath{\nu}$都是抵消的，而非首阶项只对$\ensuremath{\nu}$与能量无关|\ensuremath{\nu}|=1$ equation.其他标准的选择相对论性两体方程和影响的形式的两π交换势进行了简要讨论。
This paper begins with an explanation of the implications of the requirement that a two-body relativistic equation should approach a one-body equation when one of the masses becomes very large. It is found that the Bethe-Salpeter equation does not satisfy this requirement. An infinite family of three-dimensional equations depending on a parameter $\ensuremath{-}1\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}1$ is constructed, all of which do satisfy this limit. When $|\ensuremath{\nu}|=1$ one of the particles is on its mass shell; when $\ensuremath{\nu}=0$ both particles are equally off mass shell. The fourth order irreducible kernel for this family is studied in the expanded static limit for all $\ensuremath{\nu}$. It is found, both for scalar theories and for a realistic chiral theory of spin \textonehalf{} nucleons interacting with isovector pions, that the leading order terms in the static limit cancel for any $\ensuremath{\nu}$, and that the nonleading terms are independent of energy only for the $|\ensuremath{\nu}|=1$ equation. Other criteria for the selection of a relativistic two-body equation and implications for the form of the two-pion exchange potential are briefly discussed.