We shall recall the exact results on scattering amplitudes
and scattering cross sections which have been derived within the frame wor
ks of general field theories. Many of these results\, which have been deri
ved as bounds in the past\, can be tested against the experimental data. T
hus there is a ground to test the underlying postulates of the general fie
ld theories.

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\nNext we intend to derive some of the analyticity p
roperties of the amplitude starting from the LSZ formalism. We shall explo
re the consequences of Lorentz invariance\, microcausality and examine the
analyticity property of the amplitude. In this process we encounter the c
rossing symmetry. These properties are known as linear relations in the fo
rmal approach to field theories.

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\nWe shall study the analytici
ty 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 d
ispersion 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. T
he unitarity constraint is invoked to derive this result. We shall argue t
hat the total cross section cannot grow abritrarily for high energies. It
is bounded by the squared of the logarithm of the c.m. energy.

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\nThe dates and place are as follows:

\n**Thursday September
6 ^{th} 2018\, 11:00 – 12:00**

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\nFriday September 14

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