A Real Version of the Dirac Equation and Its Coupling to the Electromagnetic Field

• 作者: Eckart Marsch
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: DIRAC EQUATION COUPLING to Electromagnetic FIELD REAL FIELD EQUATION
• 年，卷（期）: 2015,（1）
• 页码范围: 1-11
• 页数: 11页
• 分类号: O1

摘要

A real version of the Dirac equation is derived and its coupling to the electromagnetic field considered. First the four-component real Majorana equation is briefly discussed. Then the complex Dirac equation including an electromagnetic field will be written as an eight-component real spinor equation by separating it into its real and imaginary parts. Through this decomposition, what becomes obvious is the way in which the electromagnetic field couples to charged fermions (electron and positron) when being described by real spinor fields. Thus, contrary to common expectation, charged fermions can also be described by a real Dirac equation if they are considered as a doublet related to the SO(2) symmetry group, which enables a matrix coupling to the electromagnetic field and corresponds to the usual U(1) gauge symmetry of the standard Dirac equation.