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Recent development in noncommutative geometry generalization of gauge theory is reviewed. The mathematical apparatus is reduced to minimum in order to allow the non-mathematically oriented physicists to follow the development in this interesting field of research.

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This is second of the two invited lectures presented at the “XVII International School of Theoretical Physics: Standard Model and Beyond’93.” The text is essentially based on a recent publication by the present authors [Mod. Phys. Lett. A (in press)]. Here, after briefly reviewing the \((j,0) \otimes (0,j)\) Dirac-like construct in the front form, we present a detailed construction of the \((j,0) \otimes (0,j)\) Majorana-like fields.

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We review those aspects of chiral gauge theories which are related to the violation of the decoupling property. The case of the top quark is worked out in detail. The mechanism of anomaly cancellation in the low-energy effective theory is illustrated in a simple model.

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In these lectures we review the simplest gauge extensions of the standard model, and the present and future limits on new weak interactions.

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We reemphasize the importance of discriminating fermion-loop and bosonic electroweak corrections in the analysis of electroweak precision data. Most recent data are indeed precise enough to require corrections beyond (trivial) fermion loops. An analysis of these data in terms of the observables \(\Delta x \equiv \varepsilon _{N1} - \varepsilon _{N2}\), \(\Delta y \equiv -\varepsilon _{N2}\) and \(\varepsilon \equiv -\varepsilon _{N3}\) identifies the required additional corrections as vertex corrections at the \(W^{\pm }f\bar f ^{\prime }\) and \(Z^0f\bar f\) vertices. Standard-model values for these corrections are consistent with the experimental data.

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We investigate longitudinal and transverse beam polarization in \(e^+e^- \to W^+W^-\) including electroweak radiative corrections and hard bremsstrah- lung. Also final state polarizations are discussed. We show that the transverse beam polarization allows to study the most interesting longitudinal–longitudinal final state polarization without looking at the polarization of the final state particles. However, to detect possible small deviations from the standard model a high luminosity \(e^+e^-\) collider, with energy scan from the peak of the cross-section up to about 300 GeV, is necessary.

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The present status of the calculation of the electron \(g-2\), the anomalous magnetic moment, is reviewed. An outline of the methods used in analytical calculations is given, together with a detailed exposition of the “natural variables” required to rationalize square roots of integrals required.

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We show that the supersymmetry breaking scale (\(R\)-parity), the global U(1) fermion symmetry scale and the electroweak symmetry breaking scale are strictly connected to each other.