Showing papers on "Gauge boson published in 1972"
400 citations
TL;DR: In this article, it was shown that the axial-vector current may destroy this gauge invariance in perturbation theory, even though it is present in the Lagrangian.
Abstract: Apparently nonrenormalizable field theories, such as the new models for weak interactions, can become renormalizable when gauge invariance of the second kind is present. However, the anomaly associated with the axial-vector current may destroy this gauge invariance in perturbation theory, even though it is present in the Lagrangian. When this happens the theory remains nonrenormalizable. Nevertheless it is possible, by enlarging the theory, to remove the anomaly at the expense of introducing additional fermion fields, which correspond to as-yet-unobserved particles.
310 citations
TL;DR: In this article, the spontaneously broken gauge theory is formulated in the generalized renormalizable gauge (R}_{\ensuremath{\xi}}$)-gauge, which can be adjusted to include existing gauges, $U$ gauge, $R$ gauge and 't Hooft-Feynman gauge as special cases.
Abstract: The spontaneously broken gauge theory is formulated in the generalized renormalizable gauge (${R}_{\ensuremath{\xi}}$ gauge). A parameter $\ensuremath{\xi}$ can be adjusted to include existing gauges, $U$ gauge, $R$ gauge, and 't Hooft-Feynman gauge as special cases. Three applications of the ${R}_{\ensuremath{\xi}}$-gauge formulation are given. First we compute the weak correction to the muon magnetic moment unambiguously in the existing models for leptons. Secondly, we discuss the large-momentum-transfer limit of the Pauli magnetic form factor of the muon. Finally, we discuss the static charge of the neutrino, and show that an appropriate regularization makes it vanish.
292 citations
TL;DR: In this paper, the authors identify and discuss the class of anomaly-free gauge theories with spontaneously broken gauge symmetry but without triangle anomalies, which can yield renormalizable models of weak and electromagnetic interactions.
Abstract: Theories with spontaneously broken gauge symmetry but without triangle anomalies can yield renormalizable models of weak and electromagnetic interactions. We identify and discuss the class of anomaly-free gauge theories.
164 citations
TL;DR: The second paper in this series is devoted to the formulation of a renormalizable perturbation theory of Higgs phenomena (spontaneously broken gauge theories) as discussed by the authors, in which the symmetry of the physical vacuum determines the mass spectrum of the gauge bosons.
Abstract: The second paper in this series is devoted to the formulation of a renormalizable perturbation theory of Higgs phenomena (spontaneously broken gauge theories). In Sec. II, we reformulate the renormalization prescription for massless Yang-Mills theories in terms of gauge-invariant renormalization counterterms in the action. Section III gives a group-theoretic discussion of Higgs phenomena. We discuss the possibility that an asymmetric vacuum is stable, and show how the symmetry of the physical vacuum determines the mass spectrum of the gauge bosons. We show further that in a special gauge ($U$ gauge), all unphysical fields can be eliminated. Section IV discusses the quantization of a spontaneously broken gauge theory in the $R$ gauge, where, as we show in Sec. V, Green's functions are made finite by the renormalization counterterms of the symmetric theory (in which the gauge invariance is not spontaneously broken). The $R$-gauge formulation makes use of redundant fields for the sake of renormalizability. Section VI is a discussion of the low-energy limits of propagators in the $R$-gauge formulation. In Sec. VII we show that the particles associated with redundant fields peculiar to the $R$-gauge formulation are unphysical, i.e., they do not contribute to the sum over intermediate states.
96 citations
TL;DR: The second paper in this series is devoted to the formulation of a renormalizable perturbation theory of Higgs phenomena (spontaneously broken gauge theories) as discussed by the authors, where the authors reformulate the renormalization prescription for massless Yang-Mills theories in terms of gauge-invariant counterterms in the action.
Abstract: The second paper in this series is devoted to the formulation of a renormalizable perturbation theory of Higgs phenomena (spontaneously broken gauge theories). In Sec. II, we reformulate the renormalization prescription for massless Yang-Mills theories in terms of gauge-invariant renormalization counterterms in the action. Section III gives a group-theoretic discussion of Higgs phenomena. We discuss the possibility that an asymmetric vacuum is stable, and show how the symmetry of the physical vacuum determines the mass spectrum of the gauge bosons. We show further that in a special gauge (U gauge), all unphysical fields can be eliminated. Section IV discusses the quantization of a spontaneously broken gauge theory in the R gauge, where, as we show in Sec. V, Green's functions are made finite by the renormalization counterterms of the symmetric theory (in which the gauge invariance is not spontaneously broken). The R-gauge formulation makes use of redundant fields for the sake of renormalizability. Section VI is a discussion of the low-energy limits of propagators in the R-gauge formulation. In Sec. VII we show that the particles associated with redundant fields peculiar to the R-gauge formulation are unphysical, i.e., they do not contribute to the sum over intermediate states.
73 citations
TL;DR: In this article, the authors explore the possible origin of approximate mass formulas in theories based on spontaneously broken gauge symmetry, and show that such a model is untenable in the sense that manifest breaking of the gauge symmetry would destroy the renormalizability.
Abstract: There are a number of approximate relations among elementary particle masses. In conventional theories, these are explained by assuming a hierarchy of interactions with the property that the stronger interactions have the more extensive symmetry. In renormalizable theories based on spontaneously broken gauge symmetry, this view is untenable. Manifest breaking of the gauge symmetry would destroy the renormalizability. We explore the possible origin of approximate mass formulas in theories of this kind.
70 citations
TL;DR: In this paper, it was shown that the Abelian gauge theory is renormalizable, in the sense that the Bogoliubov-Parasiuk-Hepp program can be executed in such a way that the Ward-Takahashi identities are satisfied.
Abstract: We establish that the Abelian gauge theory first considered by Higgs in which the gauge vector boson acquires a finite mass due to the spontaneous breakdown of symmetry is renormalizable, in the sense that the Bogoliubov-Parasiuk-Hepp program can be executed in such a way that the Ward-Takahashi identities are satisfied. This paper contains the global study of the Ward-Takahashi identities and low-energy theorems of the model. We show that the Goldstone boson and the scalar excitation of zero mass associated with the Landaugauge vector propagator are unphysical, and disappear from the $S$ matrix.
59 citations
TL;DR: In this article, the authors study the relationship of dual models with renormalizable theories of massive Yang-Mills fields of the type recently proposed by 't Hooft and clarify the field theoretic meaning of the twisting operator.
58 citations
TL;DR: In this article, the authors show that the Virasoro conditions in dual resonance models are related to geometrical and mechanical properties of classical two-dimensional media, and they further show that these properties are also related to the properties of the classical 2D media.
39 citations
TL;DR: In this paper, Weinberg's model of leptons is combined with the U(3) gauge model of strong interactions, and symmetry breaking for the hadrons is discussed.
Abstract: Starting from the recent U(3) $\ensuremath{\bigotimes}$ U(3) gauge model of strong interactions, we discuss the very natural synthesis with Weinberg's model of leptons. As a result of the interplay of the two models (a) neutral $\ensuremath{\Delta}S=1$ currents are eliminated without enlarging the number of quarks, and (b) a natural $(3,\overline{3})\ensuremath{\bigoplus}(3,\overline{3})$ symmetry breaking emerges for the hadrons. Incorporation of alternative lepton theories is mentioned.
TL;DR: In this paper, the authors considered the general form of the graviton propagator under an arbitrary q-number gauge transformation and showed that the potential depends only on one gauge parameter, say x. The arbitrariness of the gauge functions can be used to remove the ambiguity of the potential.
Abstract: It is believed in particle physics that the velocity-dependent part of potential is, in general, ambiguous as far as it is derived from S-matrix. We consider the most general form of the graviton ·propagator under an arbitrary q-number gauge transformation for the graviton field. The. propagator depends on twelve arbitrary functions of k 2 ,. k being the space part of the momentum . ~f the graviton. The arbitrariness of the gauge functions can be used to remove the ambiguity of orie-gni.viton exchange potential ~p to the order of (G/r) (v/c)4, G being the gravitational constant. The potential thus obtained depends only on one gauge parameter, say x. The perihelion motion of two-body system i:s gauge independent, although the potentials in the order of (G/r) (v/c) 2 and G2/r 2 depend on the gauge parameter x. The potentials are derived from those in a fixed gauge parameter x by a coordinate transformation. Suppose that we are of inter.est to obtain one-particle exchange potential between two elementary particles with masses m1 and m2. Then particle phys icists usually consider the diagram showing' that the p·articles with initial four momenta P1 and P2 and final momenta q1 and q2(P1 2 =q1 2 = -m1 2 ,P 2 2 =q 2 2 = -m 2 2 ) exchange a boson with momentum k= (PI- q1) = - CP2- q 2), and calculate the potential contributed from the S-matrix element corresp.onding to this diagram. However it is well known in particle physics that the v·elocity-dependent part of this potential is ambiguous. Since energy is conserved in any S-matrix element, t~e en.ergy transferred between two particles, ko is equal to (p 10 - q 10) and also to (q20 - p;o): The: ambiguity comes from the ko-dependence of the S-matrix element. To show this explicitly, let us consider one-graviton exchange potential be tween· two' spinless particles. The graviton propagator is proportional to \ 1
TL;DR: In this article, it is shown that the spontaneous violation of a gauge symmetry of the second kind results in the appearance not of Goldstone bosons but, rather, of massive gauge particles.
Abstract: It is known that the spontaneous violation of a gauge symmetry of the second kind results in the appearance not of Goldstone bosons but, rather, of massive gauge particles. The path-integral quantization of these theories is discussed here in general terms. The primary consideration is that quantities of physical significance, such as matrix elements of the scattering operator or the energy-momentum tensor, should be independent of the gauge in which the quantization rules are formulated. In particular, if it is possible to find one gauge in which the theory is unitary and another in which it is renormalizable, then the gauge-independent quantities must enjoy both these qualities. These ideas are applied to simple models with massive Yang-Mills fields and to a model which unifies the weak and electromagnetic interactions of electron-type leptons. Both these models appear to be unitary and renormalizable. The lepton theory is a relatively economical one. It involves five independent parameters: the electron charge and mass, the mass of the charged intermediate vector boson and the masses of a neutral scalar and a neutral vector boson.
01 Jan 1972
TL;DR: In weak-interaction theory, the most significant development in the last two years, both from purely theoretical viewpoint and from possible impact on future experiments, has been ir the construction of renormalizable models of weak interactions based on the notion of spontaneously broken gauge symmetry as discussed by the authors.
Abstract: Perhaps the most significant development In weak-interaction theory in the last two years, both from purely theoretical viewpoint and from possible impact on future experiments, has been ir. the construction of renormalizable models of weak interactions based on the notion of spontaneously broken gauge symmetry....
TL;DR: In this article, the self-consistency problem for a spinor field ψ of mass dimension 1/2 is considered in a theory with a scale-invariant nonlinear spinor equation.
Abstract: The self-consistency problem for a spinor fieldψ of mass dimension 1/2 is considered in a theory with a scale-invariant nonlinear spinor equation. It proves possible by the requirement of gauge invariance to maintain dimψ=1/2 also in a theory of interacting fields. The introduction of scale invariance breaking by massive poles into the fermion propagator makes it possible to obtain nontrivial boson solutions, especially zero-mass spin-1 bosons connected with gauge invariance of the theory. These gauge bosons couple directly only to that part of the fermion propagator which does not contain massless fermions.
TL;DR: A unified formulation of quantum electrodynamics in the generalized Lorentz gauge (including, for example, the Feynman, Landau and Yennie gauges) is presented in this paper.
Abstract: A unified formulation of quantum electrodynamics in the generalized Lorentz gauge (including, for example, the Feynman, Landau and Yennie gauges) is presented. The formulation is shown to be consistent with the appropriate commutation relations and propagators in the various gauges. All the gauge descriptions are shown to lead to Maxwell’s equations in the Lorentz gauge provided that expectation values of the electric and magnetic field intensities are taken over physically admissible states. It is shown that when the subsidiary condition is properly treated for the case of interacting photons and charged particles, the various gauge descriptions have the same physical content and electron wave function renormalization constants as the Coulomb gauge
TL;DR: In this article, a theory of interacting right-handed isospinors was extended by adding a left-hand isosinglet, which gave the possibility to construct the gauge fields of Weinberg's lepton model as bound states of these spinor fields.
Abstract: We extend a theory of interacting right-handed isospinors by adding a left-handed isosinglet. This gives the possibility to construct the gauge fields of Weinberg’s lepton model as bound states of these spinor fields. Gauge arguments are used to introduce the mass-zero photon and the weak interaction.
TL;DR: In this article, the Nambu-Jona-Lasinio model with a massless chiral gauge field and a massive vector field was investigated and symmetry breaking solutions were found in a non-covariant form.
Abstract: The Nambu-Jona-Lasinio model in which the helicity current is coupled with a massless chiral gauge field, is discussed in the pair approximation. Our model is invariant under the constant as well as local gauge transformations. We have investigated the excitation spec trum of physical states in this model, under the requirement that the chiral gauge invariance is maintained at every stage. Symmetry breaking solutions are found in a noncovariant form. Contrary to previous assertions, massless fields are still present in our theory. Thus, the physical fields are a massive vector field, a massless vector field and a phase field. It is shown that the gauge transformations are carried by the phase field and the massless vector field, respectively.
TL;DR: The implications of translational invariance and gauge invariance for an effective particle-hole interaction of the Migdal type are investigated for 208Pb in this paper, where it is shown that translational-invariant is very well satisfied while the gaugeinvariance requirement is met rather poorly.
Abstract: The implications of translational invariance and gauge invariance for an effective particle-hole interaction of the Migdal type are investigated for208Pb. It is shown that translational invariance is very well satisfied while the gauge invariance requirement is met rather poorly. Four force parameters are determined from the consistency relations for the two conservation laws.
TL;DR: In this paper, the leading divergences in the second-order weak and electromagnetic corrections to Weinberg's gauge theory are calculated in Weinberg theory and it is shown that, after renormalization, these divergencegences cancel.
Abstract: The leading (quadratic) divergences in the second-order weak and electromagnetic corrections to $\ensuremath{\mu}$ decay are calculated in Weinberg's gauge theory and it is shown that, after renormalization, these divergences cancel.
TL;DR: In this article, a 3 + 1-dimensional decomposition of a two-tensor theory of gravity was made, and the form of the constraints cast doubt on the sign of the total energy of the theory.
TL;DR: In this article, a model that unifies the intermediate boson of the weak interaction and the photon of the electromagnetic interaction into a multiplet of gauge fields is considered and the $K$-spin-triplet hypothesis emerges from such an approach.
Abstract: A model that unites the intermediate boson of the weak interaction and the photon of the electromagnetic interaction into a multiplet of gauge fields is considered. Weak leptonic currents and hadronic Cabibbo currents are handled in a parallel manner and generate an SU(2) symmetry group. It is suggested how the $K$-spin-triplet hypothesis emerges from such an approach. The symmetry between the weak and electromagnetic interaction is spontaneously broken resulting in a massive electron and an intermediate boson.
01 Jan 1972