Advances in mathematics and physics have often occurred together. The development of
Newton's theory of mechanics and the simultaneous development of the techniques of …

The article contains a systematic presentation of the covariant diagrammatic technique for
the effective action in gauge theories. The Schwinger-DeWitt technique is generalized and …

The conservation laws, such as those of charge, energy and momentum, have a central role
in physics. In some special cases, classical conservation laws are broken at the quantum …

The Quantum Theory of Fields, first published in 1996, is a self-contained, comprehensive
introduction to quantum field theory from Nobel Laureate Steven Weinberg. Volume II gives …

Chiral anomalies give rise to dissipationless transport phenomena such as the chiral
magnetic and vortical effects. In these notes I review the theory from a quantum field …

It is shown that in certain parity-violating theories in 4k+ 2 dimensions, general covariance is
spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of spin-1 2 or-3 …

We show that the mathematical relation between non-abelian anomalies in 2n dimensions,
the parity anomaly in 2n+ 1 dimensions, and the Dirac index density in 2n+ 2 dimensions …

Abstract 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 …

In 1973 two Salam protégés (Derek Capper and the author) discovered that the conformal
invariance under Weyl rescalings of the metric tensor displayed by classical massless-field …

Quantum anomalies give rise to new transport phenomena. In particular, a magnetic field
can induce an anomalous current via the chiral magnetic effect and a vortex in the relativistic …