It is shown that the path-integral measure for gauge-invariant fermion theories not invariant under ${\ensuremath{\gamma}}_{5}$ transformation and Jacobian gives rise to an extra phase factor corresponding Adler-Bell-Jackiw anomaly. The derivation of "anomalous" Ward-Takahashi identities by means variational derivative can thus be made consistent in formalism.

The Atiyah-Singer index theorem indicates that a naive unitary transformation of basis vectors for fermions interacting with gauge fields is not allowed in general. On the this observation, it was previously shown path-integral measure gauge-invariant fermion theory transformed nontrivially under chiral transformation, and thus leads to simple derivation "anomalous" Ward-Takahashi identities. We here clarify some technical aspects associated discussion. It Jacobian factor measure, which...

A massive Dirac neutrino has a magnetic moment, which causes its spin to precess in field. This reduces the effective weak cross sections for relativistic neutrinos. An estimate on basis of phenomenological considerations as well standard electroweak theory indicates that neutrinos from supernovae and neutron stars may contain significant mixtures negative- positive-helicity states.

The spontaneously broken gauge theory is formulated in the generalized renormalizable (${R}_{\ensuremath{\xi}}$ gauge). A parameter $\ensuremath{\xi}$ can be adjusted to include existing gauges, $U$ gauge, $R$ and 't Hooft-Feynman as special cases. Three applications of ${R}_{\ensuremath{\xi}}$-gauge formulation are given. First we compute weak correction muon magnetic moment unambiguously models for leptons. Secondly, discuss large-momentum-transfer limit Pauli form factor muon. Finally,...

It is shown that the trace anomaly also identified with Jacobian factor for functional measure under conformal transformation in path-integral formalism. The formulation of anomalous Ward-Takahashi identities then translated into a simple algebraic characterization chiral and anomalies. This exemplifies some common features shared by topological nontopological

A straightforward application of various regularization schemes in perturbation theory generally leads to physically unacceptable results the evaluation chiral anomaly if gauge contains ${\ensuremath{\gamma}}_{5}$ couplings. In anomaly-free properties should be imposed on all vertices, regardless whether they are vector or axial-vector, and thus (nongauge) vertex a triangle diagram could contain an couplings involve ${\ensuremath{\gamma}}_{5}$. This is illustrated by fermion number (vector)...

This study is an attempt to improve the performance of high‐temperature air cathodes by imitating porous electrodes liquid electrolyte fuel cells. Ion conductive oxides were introduced into platinum in expectation playing same electrochemical role as penetrating electrodes. The oxide‐mixed prepared modeled on a pore whose inner wall was covered with gas permeable film. An analysis based model predicted that increases increasing electrode thickness. Electrodes containing exhibited expected...

The definition of the energy-momentum tensor as a source current coupled to background gravitational field receives an important modification in quantum theory. In path-integral approach, manifest covariance integral measure under general coordinate transformations dictates that variables with weight $\frac{1}{2}$ should be used independent integration variables. An improved is then generated by variational derivative, and it gives rise well-defined conformal (Weyl) anomalies....

The field-theoretical aspects of the path integral for string Lagrangian in manner Polyakov are discussed. It is shown that Becchi-Rouet-Stora (BRS) symmetry consistent with conformal anomaly, and generalized Virasoro condition arises from BRS invariance. ghost number current, however, contains an anomaly. also noted degree freedom at $D<26$ corresponds to "unphysical" mode be canceled by Faddeev-Popov ghosts $S$ matrix conventional sense.

We show that the $\ensuremath{\xi}$-limiting regularization process of Lee and Yang can be recognized as a nonlinear gauge condition in general non-Abelian theory. The process, however, differs from gauge-invariant formulation spontaneously broken theories for finite $\ensuremath{\xi}$. Some problems related to implementation conditions are also briefly discussed.

The chiral structure of the top-bottom charged current is examined by using process $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$. new CLEO results on radiative $B$ decay constrain possible deviation from $V\ensuremath{-}A$ coupling to be less than a few percent in sector $W$ boson and top bottom quarks.

The connection between the Wess-Zumino condition and chiral anomaly is discussed in path-integral framework. When non-Abelian exists, Dirac operator detDLSL can be specified various ways. different specifications of path integral lead to forms Ward-Takahashi identities definitions composite current operators involved. imposes generalized Bose symmetry among gauge vertices, thus it introduces a particular definition operators. For example, axial-vector hypercharge an SU(3) theory, which...

In this paper we propose a definition of the regularized Jacobian coordinate Becchi-Rouet-Stora-Tyutin (BRST) transformations functional measure gravitational field and its ghosts. This allows us to prove BRST invariance reproduce known Weyl anomalies.

Some of the qualitatively new features associated with possible existence heavier Fermions in standard sequential scheme are discussed. As for heavy masses less than W-boson mass MW, weak decay constituent quarks lowest 3S1 state quarkonium is expected to become appreciable MQ ≳ 20 GeV and its implications studied. We then discuss stability Higgs mechanism presence superheavy greater MW. The interaction mediated by general becomes strong such objects, but some models as vector-like could...