Photon Propagarors in Quantum Electrodynamics

Abstract

Quantum electrodynamics in the Landau gauge is investigated in a different mann~r from Nakanishi's theory. A dipole ghost field is introduced in another simple way. It is shown that the Landau gauge representation can be obtained by a unitary transformation from the usual Feynman gauge representation. The two representations are equivalent to each other, though photon propagators take different forms superficially in each case. Supplementary conditions to eliminate the ghost states are discussed with the Lorentz condition. It is asserted that the interaction picture in the Landau gauge is also possible. *) Gota and Obara 2 ) investigated a canonical quantization method of the free electromagnetic field in the Landau gauge starting with the same field equations as those in Nakanishi's case. In their quantization the dipole ghost states are not introduced, though the longitudinal and scalar photons have peculiar characters. at Univ of Iowa-Law Library on June 7, 2015 http://ptp.oxfordjournals.org/ Downloaded from *) The q-number gauge transformation of the Green functions for charged particles was investigated by Landau and Khalatnikov. 9 ) **) The bold face letters denote the operators of the Heisenberg picture, at Univ of Iowa-Law Library on June 7, 2015 http://ptp.oxfordjournals.org/ Downloaded from

Critical Review of the Theory of Quantum Electrodynamics

“…"gaugeon" field. The Lagrangian density of the gaugeon formalism 41) [Yokoyama 1974] is obtained by further adding the gaugeon one, ^gaugeon = " **' \ C " I fe(C+YB)2 > < 4 ' 17 >…”

Gaugeon Formalism for Spin-3/2 Rarita-Schwinger Gauge Field

“…Yokoyama's gaugeon formalism [3,4,5,6,8,7] provides a wider framework in which we can consider the quantum gauge transformation among a family of Lorentz covariant linear gauges. In this formalism a set of extra fields, so called gaugeon fields, is introduced as the quantum gauge freedom.…”

“…In this formalism a set of extra fields, so called gaugeon fields, is introduced as the quantum gauge freedom. This theory was proposed for the quantum electrodynamics [3,4,5] and for the Yang-Mills theory. [6,7] Owing to the quantum gauge freedom it becomes almost trivial to check the gauge parameter independence of the physical S-matrix.…”

“…This theory was proposed for the quantum electrodynamics [3,4,5] and for the Yang-Mills theory. [6,7] Owing to the quantum gauge freedom it becomes almost trivial to check the gauge parameter independence of the physical S-matrix. [8] We should ensure that the gaugeon modes do not contribute to the physical processes.…”

“…In fact, the gaugeon fields yield negative normed states. [3] To remove these unphysical modes Yokoyama imposed a Gupta-Bleuler type subsidiary condition, [3,6,7] which is not applicable if interaction exists for gaugeon fields. Yokoyama's condition has been improved by introducing BRST symmetry for gaugeon fields.…”