Sphalerons: unsuppressed transitions between topological configurations

 Introduction

progressively updated in 2023

The transitions between states of a same system that have distinct topological properties is essentially forbidden. But in imaginary time (in Euclidean metric) transitions are possible and they are instantons. Such transitions are exponentially suppressed. However when there are thermal fluctuations transitions are possible in real time. The path (in function space) that the configuration of the system follows goes through a particular state that is unstable, static. This is sphaleron (greek: ready to fall) and may be seen as the state at the upper point of a hill (of potential) separating two states of the system.

The texts of this Section are a series of comments, evaluations, verifications, confrontation of possible approaches and selection of procedures. There is no intention to substitute textbooks or review articles and the periodic return to the orginal journal papers is highly recommended. In our meetings, repetitions and redundancies are not to be avoided.

The texts that we place here (the links below) are amorphous, prolix and incomplete. They are a simple list of problems and will be shaped through discussions. We hope that sometime they will be useful.

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 Sphalerons

Raw, elementary data on the sphalerons