Cocycles and Observers

Eberhard Zeidler
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Eberhard Zeidler: Max Planck Institute for Mathematics in the Sciences

Chapter 16 in Quantum Field Theory III: Gauge Theory, 2011, pp 871-873 from Springer

Abstract: Abstract There exist two approaches to the theory of bundles, namely, (i) the observer approach based on cocycles, and (ii) the axiomatic geometric approach. In (i), roughly speaking, we will use a cocycle in order to glue together product bundles. This will be considered in the present chapter. The geometric approach will be considered in the next chapter; this is the most elegant approach based on a few geometric axioms. For didactic reasons, we start with (i). The idea is to use bundle charts (product bundles) and to describe the change of bundle coordinates by a cocycle. In fact, the two approaches (i) and (ii) are equivalent to each other. In (ii), the cocycle corresponds to the transition maps between the bundle charts.

Keywords: Vector Bundle; Gauge Transformation; Principal Bundle; Local Observer; Elegant Approach (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-3-642-22421-8_17

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