From Thermal Field Theory to Neural Networks: A Day to Remember Tanguy Altherr

The following sections are included:

• CONTENTS

• FOREWORD

The following sections are included:

• Infra-red and mass singularities in the perturbative expansion

• Signals for the quark-gluon plasma

• Physics in dense media and applications

• Systems out of equilibrium

• Neural networks and track recognitions

• Publications by T. Altherr

Hot scalar electrodynamics is adopted as a toy model for a hot gluon plasma to display some aspects of the compulsory resummation of hard thermal loops when next-to-leading order quantities at soft momentum scales are to be calculated.

A quantum thermal field theory is constructed for scalar particles in the case of deformed statistics. The extension is provided by working out the Fock space realization of a “quantum algebra” Examining the perturbative behaviour of this theory and in particular the possible extension of the KLN theorem, we argue that it appears to be a stable structure in the context of quantum field theory¹.

Rates of photon and lepton pair emission from a QCD plasma are discussed with special emphasis on the perturbative QCD corrections. Based on these rates, estimates of lepton pair production in high energy heavy ion collisions are presented for the future colliders in Brookhaven and CERN. Recent results from the CERN SPS heavy ion experiments are briefly discussed.

In a constituent quark model at nonzero temperature, the amplitude for π⁰ → 2γ vanishes in a chirally symmetric phase, while that for π⁰σ → 2γ does not.

The following sections are included:

• Introduction

• Photons inside matter: a heuristic approach

• The electric charge of neutrinos inside a plasma

• Plasmon decay and stellar evolution

• Conclusion

• References

We have calculated axion emission from dense plasmas using thermal field theory methods. These methods are adequate for red giants and white dwarfs, as the density of both systems is very large. Although the emission rate due to the coupling with photons gets suppressed at high densities due to relativistic effects, this has no effect on the constraints on the value of the axion-photon coupling. In contrast, relativistic effects enhance the axion production due to the axion-electron coupling. From the red giants and white dwarfs evolution we obtain a conservative bound on the axion-election coupling.

In this paper I review the work on neural networks, especially the work on non-adaptive neural nets which was developed in collaboration with Tanguy Altherr.