1. Chapter V
Interacting Fields
Lecture 3
Books Recommended:
Lectures on Quantum Field Theory by Ashok
Das
Advanced Quantum Mechanics by Schwabl

2. S-matrix
At , initially particles are far apart
And non-interaction
Initial state:
Then particle come close and interact for
Short period and then after long time
they again are observed.
Particles at

3. Transition amplitude to final state
Scattering matrix or S matrix

4. In terms of Hamiltonian density
S matrix is Lorentz invariant quantity.
For QED

5. S-matrix in Unitary
Expanding asymptotic states in terms of
Complete set of final states

6. We write last Eq as
From above we write
Which shows that the unitary of S matrix
implies the conservation of probability