arXiv 2108.018532021-08-04hep-phnucl-th

Nakanishi函数方程核的新形式

New form of kernel in equation for Nakanishi function

V. A. Karmanov

备注：: 10 pages, 1 figure, accepted for publication in Phys. Rev. D
发表信息：: Phys. Rev. D 104, 056012 (2021)
DOI：: 10.1103/PhysRevD.104.056012

摘要：

Bethe-Salpeter振幅$Φ(k,p)$通过Nakanishi积分表示经由平滑函数$g(γ,z)$来表示。该函数满足正则方程$g=Ng$。然而，在这个方程中的核心$N$的计算，前面介绍，被限制到一个玻色子交换，并根据方法，处理复杂的多值函数。虽然这些困难是可以克服的，但在实践中，他们复杂的发现明确的结果。在目前的工作中，一个明确的表达的内核$N$的实函数。对于单玻色子标量交换，得到了$N$的显式表达式，并利用该表达式和核函数，重新计算了结合能。他们的发现，以及计算的贝特-萨尔彼得振幅在闵可夫斯基空间，成为不更困难的比在欧几里德之一。该方法可以推广到任何由不可约Feynman图给出的核。这种泛化是通过交叉梯形核的例子来说明的。

英文摘要：

The Bethe-Salpeter amplitude $Φ(k,p)$ is expressed, by means of the Nakanishi integral representation, via a smooth function $g(γ,z)$. This function satisfies a canonical equation $g=Ng$. However, calculations of the kernel $N$ in this equation, presented previously, were restricted to one-boson exchange and, depending on method, dealt with complex multivalued functions. Although these difficulties are surmountable, but in practice, they complicate finding the unambiguous result. In the present work, an unambiguous expression for the kernel $N$ in terms of real functions is derived. For the one-boson scalar exchange, the explicit formula for $N$ is found. With this equation and kernel, the binding energies, calculated previously, are reproduced. Their finding, as well as calculation of the Bethe-Salpeter amplitude in the Minkowski space, become not more difficult than in the Euclidean one. The method can be generalized to any kernel given by irreducible Feynman graph. This generalization is illustrated by example of the cross-ladder kernel.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文