S-matrix Theory - Basic Principles

Basic Principles

The basic principles are:

1. Relativity : The S-matrix is a representation of the Poincaré group.
2. Unitarity :
3. Analyticity : integral relations and singularity conditions

The basic analyticity principles were also called analyticity of the first kind, and they were never fully enumerated, but they include

1. Crossing: The amplitudes for antiparticle scattering are the analytic continuation of particle scattering amplitudes.
2. Dispersion relations: the values of the S-matrix can be calculated by integrals over internal energy variables of the imaginary part of the same values.
3. Causality conditions: the singularities of the S-matrix can only occur in ways that don't allow the future to influence the past (motivated by Kramers Kronig dispersion relation)
4. Landau Principle: Any singularity of the S-matrix corresponds to production thresholds of physical particles.

These principles were to replace the notion of microscopic causality in field theory, the idea that field operators exist at each space time point, and that spacelike separated operators commute with one another.