ON GAUGE INVARIANCE AND VACUUM POLARIZATION
ON GAUGE INVARIANCE AND VACUUM POLARIZATION
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DOI：
10.1103/physrev.82.664
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发表时间：
1951-01-01
期刊：
影响因子：
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通讯作者：
SCHWINGER, J
中科院分区：
文献类型：
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作者：
SCHWINGER, J
本文是基于基本的意见，规范不变的提取结果从正式规范不变的理论是确保如果采用的解决方案，只涉及规范协变量的方法。我们用一个规定的电磁场引起的真空极化问题来说明这一说法。带电狄拉克场的真空电流可以用该场的绿色函数表示，它意味着电磁场作用量积分的增加。现在，这些量可以与“粒子”的动力学性质相关，其时空坐标取决于固有时间参数。本时运动方程只涉及电磁场强度，为处理问题提供了合适的规范不变基础。对于常量场和平面波场，可以得到运动方程的严格解。一个重整化的场强和电荷，适用于修改后的拉格朗日函数的恒定字段，产生一个有限的，规范不变的结果，这意味着在真空中的电磁场的非线性特性。零自旋带电场的贡献也被陈述。经过相同场强重整化后，描述真空中平面波的修改物理量减少到麦克斯韦场的物理量;对于任意强度和谱组成的单个平面波，不存在非线性现象。然后，将常数（即缓慢变化的场）获得的结果应用于处理由质子真空极化引起的自旋零中性介子的双光子衰变。我们得到近似的，规范不变的表达式介子和电磁场之间的有效相互作用，其中核耦合可以是标量，赝标量，或赝矢量的性质。直接验证赝标量和赝矢量相互作用之间的等价性只需要对所涉及的极限过程作适当的说明。对于任意变化的场，如附录A所讨论的，可以将摄动法应用于运动方程，或者可以采用势矢量的幂展开。后者自动产生规范不变的结果，只要适当的时间积分是保留到最后。这表明，适当的时间方法的重要方面是它的隔离发散积分的适当的时间参数，这是独立的坐标系和规范。讨论了固有时间方法与“不变正则化”技术之间的联系。顺便说一句，实际对产生的概率是从电磁场作用积分的虚部获得的。最后，作为常场绿色函数的一个应用，我们构造了均匀弱外场中电子的质量算符，并通过微扰计算得到了α 2 π磁子的附加自旋磁矩。在微扰计算中，固有质量通常起能量的作用。
This paper is based on the elementary remark that the extraction of gauge invariant results from a formally gauge invariant theory is ensured if one employs methods of solution that involve only gauge covariant quantities. We illustrate this statement in connection with the problem of vacuum polarization by a prescribed electromagnetic field. The vacuum current of a charged Dirac field, which can be expressed in terms of the Green's function of that field, implies an addition to the action integral of the electromagnetic field. Now these quantities can be related to the dynamical properties of a" particle" with space-time coordinates that depend upon a proper-time parameter. The proper-time equations of motion involve only electromagnetic field strengths, and provide a suitable gauge invariant basis for treating problems. Rigorous solutions of the equations of motion can be obtained for a constant field, and for a plane wave field. A renormalization of field strength and charge, applied to the modified lagrange function for constant fields, yields a finite, gauge invariant result which implies nonlinear properties for the electromagnetic field in the vacuum. The contribution of a zero spin charged field is also stated. After the same field strength renormalization, the modified physical quantities describing a plane wave in the vacuum reduce to just those of the maxwell field; there are no nonlinear phenomena for a single plane wave, of arbitrary strength and spectral composition. The results obtained for constant (that is, slowly varying fields), are then applied to treat the two-photon disintegration of a spin zero neutral meson arising from the polarization of the proton vacuum. We obtain approximate, gauge invariant expressions for the effective interaction between the meson and the electromagnetic field, in which the nuclear coupling may be scalar, pseudoscalar, or pseudovector in nature. The direct verification of equivalence between the pseudoscalar and pseudovector interactions only requires a proper statement of the limiting processes involved. For arbitrarily varying fields, perturbation methods can be applied to the equations of motion, as discussed in Appendix A, or one can employ an expansion in powers of the potential vector. The latter automatically yields gauge invariant results, provided only that the proper-time integration is reserved to the last. This indicates that the significant aspect of the proper-time method is its isolation of divergences in integrals with respect to the proper-time parameter, which is independent of the coordinate system and of the gauge. The connection between the proper-time method and the technique of" invariant regularization" is discussed. Incidentally, the probability of actual pair creation is obtained from the imaginary part of the electromagnetic field action integral. Finally, as an application of the Green's function for a constant field, we construct the mass operator of an electron in a weak, homogeneous external field, and derive the additional spin magnetic moment of α 2 π magnetons by means of a perturbation calculation in which proper-mass plays the customary role of energy.