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首页> 外文期刊>Zeitschrift fur Naturforschung. A, A journal of physical sciences >Resolution of constraints and gauge equivalence in algebraic Schroedinger representation of quantum electrodynamics
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Resolution of constraints and gauge equivalence in algebraic Schroedinger representation of quantum electrodynamics

机译：量子电动力学的代数Schroedinger表示中的约束和规范等效项的解析

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摘要

The algebraic formalism of QED is expounded in order to demonstrate both the resolution of constraints and to verify gauge equivalence between temporal gauge and Coulomb gauge on the quantum level. In the algebraic approach energy eigenstates of QED in temporal gauge are represented in an algebraic GNS basis. The corresponding Hilbert space is mapped into a functional space of generating functional states. The image of the QED-Heisenberg dynamics becomes a functional energy equation for these states. In the same manner the Gauss constraint is mapped into functional space. By suitable transformations the functional image of the Coulomb forces is recovered in temporal gauge. The equivalence of this result with the functional version of QED in Coulomb gauge is demonstrated. The meaning of the various transformations and their relations are illustrated for the case of harmonic oscillators. If applied to QCD this method allows an exact derivation of effective color "Coulomb" forces, in addition it implies a clear conception for the incorporation of various algebraic representations into the formal Heisenberg dynamics and establishes the algebraic "Schroedinger" equation for quantum fields in functional space.
机译：阐述了QED的代数形式，以证明约束的解析并在量子水平上验证时间轨距和库仑轨距之间的轨距等效。在代数方法中，时标中QED的能量本征态以代数GNS表示。对应的希尔伯特空间被映射到生成功能状态的功能空间中。 QED-海森堡动力学的图像成为这些状态的函数能量方程。以相同的方式将高斯约束映射到功能空间。通过适当的变换，可以在时间范围内恢复库仑力的功能图像。证明了该结果与库仑量规中QED的功能版本的等效性。对于谐波振荡器，说明了各种变换的含义及其关系。如果将其应用于QCD，则该方法可以精确推导有效的颜色“库仑”力，此外，它还暗示了将各种代数表示形式并入正式的Heisenberg动力学的清晰概念，并为功能量子场建立了代数“ Schroedinger”方程空间。

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