The Analytic S-matrix

Alexander Zhiboedov (CERN)

2020-04-24 00:00, Salle Itzykson, IPhT
Approved by the École Doctorale ED PIF


The bootstrap approach asserts that certain physical theories can be strongly constrained, and sometimes even be solved, using general principles only. We review old and new results obtained from applying this approach to scattering of relativistic, massive particles in flat space.

The S-matrix describes transitions between states of freely moving particles in the far past and the distant future. Conventionally such transitions, or scattering amplitudes, are computed in perturbation theory. The S-matrix bootstrap is a program of constructing scattering amplitudes nonperturbatively based on general principles of special relativity and quantum mechanics.

The aim of the course is two-fold. First, we review the classical results of the S-matrix theory and their connection to the basic principles of relativistic QFT, such as causality, locality and unitarity. This will lead us to the formulation of the S-matrix bootstrap problem and derivations of various classical results of the S-matrix theory that concern nonperturbative properties of scattering amplitudes. Second, we go over various attempts to construct scattering amplitudes that satisfy the desired properties and more humbly obtain rigorous nonperturbative bounds on such amplitudes. These include both ideas from half a century ago (when most of the classic results were first derived), as well as recent efforts to rejuvenate the S-matrix bootstrap program.

Plan of the course:

  1. Introduction to the S-matrix theory.
  2. Kinematics (Mandelstam plane, unitarity, crossing, partial waves).
  3. Analyticity (field theory analyticity, analytic completion, unitarity extension of analyticity).
  4. Universal Bounds (Froissart-Gribov formula, Mandelstam kernel, Martin-Froissart bound, Gribovs theorem, Dragt bootstrap).
  5. Bootstrap Methods (elastic unitarity, saturation of the Froissart bound, coupling maximization).



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