an article that we are finalizing at CQTS:
Hisham Sati and Urs Schreiber:
Quantum Observables of Quantized Fluxes
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pdf (v2)
Abstract. While it has become widely appreciated that defining (higher) gauge theories requires, in addition to ordinary phase space data, also “flux quantization” laws in generalized differential cohomology, there has been little discussion of the general rules, if any, for lifting Poisson-brackets of (flux-)observables and their quantization from ordinary phase spaces to the resulting higher moduli stacks of flux-quantized gauge fields.
In this short note we present a systematic analysis of (i) the canonical quantization of flux observables in Yang-Mills theory and (ii) of valid flux quantization laws in abelian Yang-Mills. We observe (iii) that the resulting topological quantum observables form the homology Pontrjagin algebra of the loop space of the moduli space of flux-quantized gauge fields.
This is remarkable because the homology Pontrjagin algebra on loops of moduli makes immediate sense in broad generality for higher and non-abelian (non-linearly coupled) gauge fields, such as for the C-field in 11d supergravity, where it recovers the quantum effects previously discussed [I, II] in the context of “Hypothesis H”.
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Last revised on April 3, 2024 at 12:30:02. See the history of this page for a list of all contributions to it.