We review the covariant formulation of quantum field theory, and in particular DeWitt's
background field method, Schwinger's proper-time representations and Pauli-Villars …

Berry's phase (1, 2) is an example of holonomy, the extent to which some variables change
when other variables or parameters characterizing a system return to their initial values (3 …

Recently, Berry recognized in quantum mechanics a topological phase factor arising from
the adiabatic transport of a system around a closed circuit, which is essentially the Aharonov …

Now in paperback, this book provides a self-contained introduction to the cohomology
theory of Lie groups and algebras and to some of its applications in physics. No previous …

The effective action induced by chiral fermions can be written, formally, as an overlap of two
states. These states are the Fock ground states of hamiltonians for fermions in even …

A relativistic quantum field theory provides a dynamical framework for explaining a vast
variety of physical phenomena: not only are all properties of bound and scattering states …

We trace the origin of θ-terms in nonlinear σ-models as a nonperturbative anomaly of current
algebras. The nonlinear σ-models emerge as a low energy limit of fermionic σ-models. The …

A mathematical treatment is presented of the known Berry, Wilczek-Zee, Aharonov-
Anandan, and Pancharatnam topological phases, and simple illustrative examples of their …

We discuss how symmetries and conservation laws are affected when Berry's phase occurs
in a quantum system: symmetry transformations of coordinates have to be supplemented by …

The authors derive, by a biorthonormal state approach, the analogy of Berry's phase factor
for open, non-conservative systems, for both adiabatic and non-adiabatic evolution. In the …