507 research outputs found
Index Theorems and Domain Walls
The Atiyah-Patodi-Singer (APS) index theorem relates the index of a Dirac
operator to an integral of the Pontryagin density in the bulk (which is equal
to global chiral anomaly) and an invariant on the boundary (which
defines the parity anomaly). We show that the APS index theorem holds for
configurations with domain walls that are defined as surfaces where background
gauge fields have discontinuities.Comment: 11+1 pages, v2: a reference adde
Heat Trace Asymptotics on Noncommutative Spaces
This is a mini-review of the heat kernel expansion for generalized Laplacians
on various noncommutative spaces. Applications to the spectral action
principle, renormalization of noncommutative theories and anomalies are also
considered.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
The Faddeev-Popov trick in the presence of boundaries
We formulate criteria of applicability of the Faddeev-Popov trick to gauge
theories on manifolds with boundaries. With the example of Euclidean Maxwell
theory we demonstrate that the path integral is indeed gauge independent when
these criteria are satisfied, and depends on a gauge choice whenever these
criteria are violated. In the latter case gauge dependent boundary conditions
are required for a self-consistent formulation of the path intgral.Comment: LaTEX, 10p
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