Gauge theory

About: Gauge theory is a research topic. Over the lifetime, 38727 publications have been published within this topic receiving 1205810 citations. The topic is also known as: Gauge symmetry.

On gauge invariance and vacuum polarization

Abstract: 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 $\frac{\ensuremath{\alpha}}{2\ensuremath{\pi}}$ magnetons by means of a perturbation calculation in which proper-mass plays the customary role of energy.

CP Violation in the Renormalizable Theory of Weak Interaction

Abstract: In a framework of the renormalizable theory of weak interaction, problems of CP-violation are studied. It is concluded that no realistic models of CP-violation exist in the quartet scheme without introducing any other new fields. Some possible models of CP-violation are also discussed. When we apply the renormalizable theory of weak interaction1l to the hadron system, we have some limitations on the hadron model. It is well known that there exists, in the case of the triplet model, a difficulty of the strangeness chang­ ing neutral current and that the quartet model is free from this difficulty. Fur­ thermore, Maki and one of the present authors (T.M.) have shown2l that, in the latter case, the strong interaction must be chiral SU ( 4) X SU ( 4) invariant as precisely as the conservation of the third component of the iso-spin 13 • In addi­ tion to these arguments, for the theory to be realistic, CP-violating interactions should be incorporated in a gauge invariant way. This requirement will impose further limitations on the hadron model and the CP-violating interaction itself. The purpose of the present paper is to investigate this problem. In the following, it will be shown that in the case of the above-mentioned quartet model, we cannot make a CP-violating interaction without introducing any other new fields when we require the following conditions: a) The mass of the fourth member of the quartet, which we will call (, is sufficiently large, b) the model should be con­ sistent with our well-established knowledge of the semi-leptonic processes. After that some possible ways of bringing CP-violation into the theory will be discussed. We consider the quartet model with a charge assignment of Q, Q -1, Q -1 and Q for p, n, A. and (, respectively, and we take the same underlying gauge group SUweak (2) X SU(1) and the scalar doublet field cp as those of Weinberg's original model.1l Then, hadronic parts of the Lagrangian can be devided in the following way:

An Introduction to Quantum Field Theory

Abstract: Feynman Diagrams and Quantum Electrodynamics * Invitation: Pair Production in e+e- Annihilation * The Klein-Gordon Field * The Dirac Field * Interacting Fields and Feynman Diagrams * Elementary Processes of Quantum Electrodynamics * Radiative Corrections: Introduction * Radiative Corrections: Some Formal Developments * Final Project: Radiation of Gluon Jets Renormalization * Invitation: Ultraviolet Cutoffs and Critical Fluctuations * Functional Methods * Systematics of Renormalization * Renormalization and Symmetry * The Renormalization Group * Critical Exponents and Scalar Field Theory * Final Project: The Coleman-Weinberg Potential Non-Albelian Gauge Theory * Invitation: The Parton Model of Hadron Structure * Non-Albein Gauge Invariance * Quantization of Non-Abelian Gauge Theories * Quantum Chromodynamics * Operator Products and Effective Vertices * Perturbation Theory Anomalies * Gauge Theories with Spontaneous Symmetry Breaking * Quantization of Spontaneously Broken Gauge Theories * Final Project: Decays of the Higgs Boson * Epilogue: Field Theory at the Frontier

Broken Symmetries and the Masses of Gauge Bosons

Abstract: In a recent note' it was shown that the Goldstone theorem, ' that Lorentz-covaria. nt field theories in which spontaneous breakdown of symmetry under an internal Lie group occurs contain zero-mass particles, fails if and only if the conserved currents associated with the internal group are coupled to gauge fields. The purpose of the present note is to report that, as a consequence of this coupling, the spin-one quanta of some of the gauge fields acquire mass; the longitudinal degrees of freedom of these particles (which would be absent if their mass were zero) go over into the Goldstone bosons when the coupling tends to zero. This phenomenon is just the relativistic analog of the plasmon phenomenon to which Anderson' has drawn attention: that the scalar zero-mass excitations of a superconducting neutral Fermi gas become longitudinal plasmon modes of finite mass when the gas is charged. The simplest theory which exhibits this behavior is a gauge-invariant version of a model used by Goldstone' himself: Two real' scalar fields y„y, and a real vector field A interact through the Lagrangian density