Renormalization Of Gauge Theories Research Articles

Renormalization of gauge theories

Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts. These identities are proved to all orders of renormalized perturbation theory, within the BPHZ framework, when the underlying Lie algebra is semisimple and the gauge function is chosen to be linear in the fields in such a way that all fields are massive. An example, the SU2 Higgs Kibble model is analyzed in detail: the asymptotic theory is formulated in the perturbative sense, and shown to be reasonable, namely, the physical S operator is unitary and independent from the parameters which define the gauge function.

Vector model of the weak interactions

We search for a renormalizable gauge theory incorporating our modified weak current. The right-handed quarks participate to give a natural explanation for the nonleptonic $\ensuremath{\Delta}I=\frac{1}{2}$ rule. We argue that extra quarks and/or extra leptons are necessary. We focus on a vector-like model involving six different quark flavors, each in a color triplet: 18 quarks all told. The model also involves a third charged lepton and several massive neutral leptons. We compare the predictions of our model with the conventional (12 quarks) model. Present experimental data are insufficient to discriminate between the two models. We give detailed analyses and predictions concerning charged-current and neutral-current phenomena, including inclusive scattering, scattering of neutrinos by electrons, single-pion production, and neutrino or antineutrino elastic scattering on protons.

Stellar Cooling in Gauge Theories of Weak Interactions

view Abstract Citations (2) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Stellar Cooling in Gauge Theories of Weak Interactions Mikaelian, Karnig O. Abstract We consider a large class of processes leading to stellar energy loss, and derive general rules relating the rates in the ordinary V - A theory to those of renormalizable gauge theories of weak and electromagnetic interactions. In these theories energy loss to both electron-type and muontype neutrinos is allowed. Assuming i -e universality, the rates attain their minimum for certain values (approximately realized in the Weinberg model) of the neutral-current couplings. More general results, without the assumption of -e universality, are also stated. Subject headings: interiors, stellar - neutrinos - nuclear reactions Publication: The Astrophysical Journal Pub Date: September 1975 DOI: 10.1086/153792 Bibcode: 1975ApJ...200..336M full text sources ADS |

Incorporation ofCPviolation with a unified renormalizable gauge theory

A unified renormalizable gauge theory with $\mathrm{CP}$ violation is presented without having to introduce heavy leptons. The theory utilizes three triples of quarks and three charmed quarks. Models in the SU(2) \ifmmode\times\else\texttimes\fi{} U(1) and SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge groups are constructed. The $\mathrm{CP}$-violating phases are in the hadronic sector which is partly composed of a mixture of two triples. The lepton-hadron anomaly cancellation mechanism is adopted, and a superweak type of $\mathrm{CP}$ violation results from the model.

Scaling properties of a gauge theory with Han-Nambu quarks and charged vector gluons

A renormalizable gauge theory of strong and electromagnetic interactions with integrally charged quarks is constructed, and its scaling behavior is analyzed.

Renormalizable gauge theories with nonlinear constraints

We discuss a class of gauge theories with nonlinear constraints which are equivalent to renormalizable theories with gauge groups of the form $G\ensuremath{\bigotimes}{G}^{\ensuremath{'}}$ in the limit as one of the charges vanishes. Such theories may be useful in obtaining natural zeroth-order symmetries without introducing strangeness-carrying neutral currents.

Reggeization of elementary particles in renormalizable gauge theories: Scalars

Reggeization of elementary particles in renormalizable gauge theories: Scalars

Renormalization of gauge theories—unbroken and broken

A comprehensive discussion is given of the renormalization of gauge theories, with or without spontaneous breakdown of gauge symmetry. The present discussion makes use of the Ward-Takahashi identities for proper vertices (as opposed to the identities for Green's functions) recently derived. The following features of the present discussion are significant: (1) The present discussion applies to a very wide class of gauge conditions. (2) The present discussion applies to any gauge group and any representation of the scalar fields. (3) The renormalized S matrix is shown to be gauge-independent. (4) Dependence of counterterms on the gauge chosen is discussed.

Reggeization of Elementary Particles in Renormalizable Gauge Theories: Vectors and Spinors

The question of the Reggeization of the elementary particles in renormalizable gauge theories with the Higgs-Kibble mechanism is examined. It is concluded that the massive non-Abelian gauge vector mesons and $J=\frac{1}{2}$ fermions of these theoreis lie on Regge trajectories in every case in which a counting criterion due to Mandelstam is satisfied. Several explicit examples are presented which verify that the necessary factorization condition of the Born helicity matrices is satisfied at $J=1$ and $J=\frac{1}{2}$, supporting this conclusion.

Renormalizability of Gauge Theories with Spontaneously Broken Discrete Symmetries

It is shown that a large class of global symmetries, including the physically interesting discrete symmetries, may be broken spontaneously in gauge theories without destroying renormalizability.

Constraints on Higgs Fields in Unified Weak-Electromagnetic Gauge Theories

In renormalizable unified gauge theories of the weak and electromagnetic interactions, for a given gauge group we ask the following question: Which representations of the scalar Higgs particles can reproduce a vector-meson mass spectrum in which one vector meson, the photon, remains massless and all other vector mesons acquire mass? Given the Higgs representation, we then examine what restrictions are placed on the charge operator of the theory. The examples of SU(3) and SU(3) \ifmmode\times\else\texttimes\fi{} U(1) are worked out in detail. The possible Higgs representations for all the unexceptional classical Lie groups are given. For each such group, there are some low-dimensional representations for which no solution exists.

ΔI=12Rule in a Gauge Model

We present a formulation of the schizon scheme of Lee and Yang which is within the framework of a renormalizable gauge theory and which yields the full octet rule at the SU(3) level. The model contains six massive gauge fields, two charged and four neutral.

Current Algebra and Gauge Theories. I

The methods of current algebra are applied to the problem of calculating corrections to the symmetries of the strong interactions in renormalizable gauge theories of the weak and electromagnetic interactions. The strong interactions are described by a neutral-vector-gluon model, so that their symmetries are just the symmetries of the quark mass matrix, and are determined by the vacuum expectation values of the weakly coupled scalar fields. Corrections to these symmetries are calculated to all orders in the gluon coupling, but only to second order in the gauge coupling $e$. After putting the results in a gauge-invariant form, it is found that all divergences cancel in the corrections to "natural" symmetries of the strong interactions. The weak interactions can produce corrections to strong-interaction symmetries of the same order of magnitude as the electromagnetic corrections, but such "order $\ensuremath{\alpha}$" effects occur only as corrections to the quark mass matrix, and therefore necessarily conserve parity, strangeness, charm, etc., and may produce only isovector corrections to isotopic-spin conservation. It is suggested that these weak-interaction effects of order $\ensuremath{\alpha}$ are responsible for the nonelectromagnetic corrections to isotopic-spin conservation which seem to be needed in calculations of mass differences and $\ensuremath{\eta}$ decay.

Perturbative Calculations of Symmetry Breaking

The one-loop contributions to fermion and pseudo-Goldstone masses are calculated for the general class of renormalizable guage theories. It is shown explicitly that when the masses are subject to any type of zeroth-order symmetry. relation for all values of the parameters in the Lagrangian, the divergences in the one-loop corrections to these symmetry relations cancel. The finite parts of these corrections are evaluated and discussed. Other topics considered include the connection of this work with that of Coleman and E. Weinberg, the constraints obeyed by scalar coupling constants, and the path-integral derivation of the Feynman rules for general renormalizable gauge theories.

Renormalizability of Gauge Theories

By generalization of methods developed by Kamefuchi, O'Raifeartaigh, and Salam, conditions for renormalizability of general gauge theories of massive vector mesons are derived. These conditions are stated explicitly in Eqs. (39) and (40) of the text. It is shown that all theories based on simple Lie groups (with the one exception of the neutral vector meson theory in interaction with a conserved current) are unrenormalizable.