Schreiber Quantum Observables of Quantized Fluxes

an article that we have written at CQTS:

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• Hisham Sati$\;$ and $\;$ Urs Schreiber:

  
  

  Quantum Observables of Quantized Fluxes

  
  

  Annales Henri Poincaré (2024)

  doi:10.1007/s00023-024-01517-z

  
  

  download:

  • pdf (v2)

  • arXiv:2312.13037

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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Companion article:

• Flux Quantization on Phase Space

Related articles:

• Differential Cohomotopy implies intersecting brane observables

• Fundamental weight systems are quantum states

• Flux Quantization on M5-Branes

• Flux Quantization on Holographic M5-Branes

• Introduction to Hypothesis H