Journal ArticleDOI
A relation between group‐ and Čech‐cohomology in principal fiber bundles and anomalies
TLDR
In this paper, a natural map between group cohomology of the structure group of a principal fiber bundle with coefficients in the space of functions from the total space into an Abelian group and Cech-cohomology in the base space is defined.Abstract:
A natural map between group‐cohomology of the structure group of a principal fiber bundle with coefficients in the space of functions from the total space into an Abelian group and Cech‐cohomology of the base space is defined. A differential complex of local group‐cochains is constructed and an analog of the Poincare lemma for group‐cohomology is proven. By using the machinery of spectral sequences the cohomology of this complex is calculated and the connection between group‐cohomology and Cech‐cohomology of the given principal fiber bundle is elucidated. Finally, the non‐Abelian and Witten anomaly in this context is reviewed and the relevance of our results for lifting principal group actions is discussed.read more
Citations
More filters
Journal ArticleDOI
Cohomology and topological anomalies
TL;DR: In this article, the chiral anomaly can be considered as an object defined either on the space of gauge potentials or on the orbit space, and the relation between the two descriptions is discussed.
References
More filters
Journal ArticleDOI
An SU(2) anomaly
TL;DR: In this paper, a new restriction of fermion quantum numbers in gauge theories is derived, and it is shown that an SU(2) gauge theory with an odd number of left-handed fermions doublets is mathematically inconsistent.
Journal ArticleDOI
Operator anomaly for the gauss law
TL;DR: In this paper, it was shown that a Schwinger term can appear in the commutation relations of constraints for the theory of the interacting Yang-Mills field and chiral fermions.
Journal ArticleDOI
Dirac operators coupled to vector potentials
TL;DR: Characteristic classes for the index of the Dirac family [unk](A) are computed in terms of differential forms on the orbit space of vector potentials under gauge transformations to represent obstructions to the existence of a covariant Dirac propagator.
Journal ArticleDOI
BRS cohomology and topological anomalies
Gregorio Falqui,Cesare Reina +1 more
TL;DR: In this article, the authors make contact between this approach and BRS cohomology, by showing that they yield the same non-abelian anomalies, provided a certain restriction to local functionals is not introduced from the very beginning.
Journal ArticleDOI
Group actions and anomalies in gauge theories
TL;DR: In this article, the transformation properties of the vacuum functional W ( A ) for chiral fermions in a gauge potential A under the group A ×U(1)× R + of gauge, chiral and scale transformations are studied.
Related Papers (5)
A new geometric invariant associated to the space of flat connections
K. Guruprasad,Shrawan Kumar +1 more