Bayesian inference of non-positive spectral functions in quantum field theory

Abstract

We present the generalization to non positive definite spectral functions of a recently proposed Bayesian deconvolution approach (BR method). The novel prior used here retains many of the beneficial analytic properties of the original method, in particular it allows us to integrate out the hyperparameter $\alpha$ directly. To preserve the underlying axiom of scale invariance, we introduce a second default-model related function, whose role is discussed. Our reconstruction prescription is contrasted with existing direct methods, as well as with an approach where shift functions are introduced to compensate for negative spectral features. A mock spectrum analysis inspired by the study of gluon spectral functions in QCD illustrates the capabilities of this new approach.

14 pages, 15 figures

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• Quantum mechanical limitations to spin diffusion in the unitary Fermi gas
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• The QCD moat regime and its real-time properties
• Bayesian inference of real-time dynamics from lattice QCD
• TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data
• Analytic continuation and physical content of the gluon propagator
• Taming numerical imprecision by adapting the KL divergence to negative probabilities