Quantum Effects on Four-Dimensional Space-Time Symmetries

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Abstract
It is shown that, in gauge theories of chiral Weyl fermions, quantum effects can induce breakdowns of relativistic space-time symmetries in four dimensions. These so-called "anomalies" are caused by U(1) gauge fields, and in combination with gravitational field; non-Abelian gauge fields have no effect. In the standard Glashow-Weinberg-Salam SU(2) ⊗ U(1) model, the U(1) charges of the chiral fermions are such that, within each family, these relativistic anomalies cancel out for leptons and quarks separately.