Analyticity Properties and Behavior of Scattering Amplitude at Asymptotic Energies

We shall recall the exact results on scattering amplitudes and scattering cross sectionswhich have been derived within the frame works of general field theories. Many of these results, which have been derived as bounds in the past, can be tested against theexperimental data. Thus there is a ground to test the underlying postulates of the general
field theories.

Next we intend to derive some of the analyticity properties of the amplitude starting from the LSZ formalism. We shall explore the consequences of Lorentz invariance, microcausality and examine the analyticity property of the amplitude. In this process we encounter the crossing symmetry. These properties are known as linear relations in the formal approach to field theories.

We shall study the analyticity of the amplitude for fixed momentum transfer,t and we shall argue that there is a region, -T<t<0 within which the amplitude satisfies dispersion relation in s. We shall explore a domain which is direct product of the cut s-plane and a domain in t-plane where amplitude is analytic. The unitarity constraint is invoked to derive this result. We shall argue that the total cross section cannot grow abritrarily for high energies. It is bounded by the squared of the logarithm of the c.m. energy.

The dates and place are as follows:

Thursday September 6th 2018, 11:00 – 12:00
Thursday September 13th 2018, 11:00 – 12:00
Friday September 14th 2018, 11:00 – 12:00

BSP 727 Cubotron / UNIL