In quantum field theory (QFT), amplitudes represent probabilities or likelihoods of different particle interactions or processes. They provide a way to calculate the likelihoods of various outcomes or transitions between different states of particles.
In QFT, particles are treated as excitations of underlying fields. These fields pervade all of spacetime and are described by quantum mechanical operators. The interactions between particles are described by the interactions of these fields.
Amplitudes are calculated using Feynman diagrams, which are graphical representations of particle interactions. Each Feynman diagram represents a possible way in which particles can interact or transition between different states. The amplitudes associated with Feynman diagrams are calculated by summing over all possible paths or processes contributing to the given interaction.
The square of the amplitude gives the probability density for a particular outcome or transition to occur. By summing over all possible paths or processes, one obtains the total probability for the interaction or process to happen.
Amplitudes in QFT are influenced by several factors, including the coupling strengths of the interacting fields, the momenta and spins of the particles involved, and the conservation laws of various quantities, such as energy, momentum, and charge. These factors determine the relative probabilities of different outcomes or transitions.
Amplitudes play a crucial role in calculating various observables in QFT, such as scattering cross-sections or decay rates. They allow us to make predictions and compare them with experimental results, providing a way to test the validity and accuracy of the theory.
In summary, amplitudes in QFT represent the probabilities or likelihoods of different particle interactions or processes. They are calculated using Feynman diagrams and play a central role in making predictions and understanding the behavior of particles in quantum field theory.