In quantum field theory (QFT), amplitudes represent the probabilities of different particle interactions and processes. QFT describes the behavior of elementary particles and their interactions through quantum fields that permeate all of spacetime.
In the framework of QFT, particles are considered as excitations or quanta of their respective fields. These fields are defined at every point in spacetime, and their behavior is governed by equations such as the Klein-Gordon equation, the Dirac equation, or the Yang-Mills equations, depending on the specific field involved.
Amplitudes in QFT are typically expressed as mathematical quantities called scattering amplitudes. Scattering amplitudes provide the probability amplitudes for various particle interactions to occur. They describe the likelihood of initial particles transforming into final particles through a scattering process, where the particles involved exchange energy, momentum, and other quantum properties.
The calculation of scattering amplitudes involves summing over all possible intermediate states and interactions that can occur between the initial and final particles. Feynman diagrams, which are graphical representations of particle interactions, are often used to visualize and calculate these amplitudes.
The square of the scattering amplitude gives the probability of the corresponding interaction happening. The amplitudes are complex numbers, and the squared magnitude of the amplitude gives the probability density of the interaction.
It's important to note that amplitudes in QFT are not directly observable quantities. Instead, they are used to calculate probabilities that can be compared with experimental measurements. By comparing the theoretical predictions with experimental data, physicists can test the validity of QFT and gain insights into the fundamental interactions and particles of the universe.