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Effective theories of connections and curvature: Abelian case.
- Source :
-
Journal of Mathematical Physics . May2012, Vol. 53 Issue 5, p052301. 24p. - Publication Year :
- 2012
-
Abstract
- We introduce a notion of measuring scales for quantum Abelian gauge systems. At each measuring scale a finite dimensional affine space stores information about the evaluation of the curvature on a discrete family of surfaces. Affine maps from the spaces assigned to finer scales to those assigned to coarser scales play the role of coarse graining maps. This structure induces a continuum limit space which contains information regarding curvature evaluation on all piecewise linear surfaces with boundary. The evaluation of holonomies along loops is also encoded in the spaces introduced here; thus, our framework is closely related to loop quantization and it allows us to discuss effective theories in a sensible way. We develop basic elements of measure theory on the introduced spaces which are essential for the applicability of the framework to the construction of quantum Abelian gauge theories. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 53
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 76272916
- Full Text :
- https://doi.org/10.1063/1.4705391