In Quantum Field Theory (QFT), particles are considered excitations or disturbances in their corresponding quantum fields. These fields permeate all of spacetime, and particles arise as localized vibrations or disturbances in these fields. However, it's important to note that particles in QFT are not the same as classical particles in everyday experience.
In quantum mechanics, the behavior of particles is described by wave functions, which are mathematical objects that encode the probabilities of different outcomes when measurements are made. Wave functions can undergo a process called "wave function collapse" or "measurement" when a particle's properties are measured, resulting in a definite outcome. After the collapse, the particle is described by a specific state.
In the context of QFT, particles are not considered to be "real" in the same sense as classical particles with definite positions and velocities. Instead, they are understood as specific excitations or localized disturbances in the underlying quantum fields. These excitations or disturbances are quantized and can be described as quanta of energy associated with their respective fields.
Regarding scattering amplitudes, they are fundamental quantities in QFT that describe the probabilities or amplitudes of different particles undergoing scattering processes. Scattering occurs when particles interact and change their states as a result of this interaction. Scattering amplitudes are calculated using Feynman diagrams, which are graphical representations of the interactions between particles.
In summary, in QFT, particles are considered localized excitations in quantum fields, and their behavior is described by wave functions. After wave function collapse, the particle is described by a specific state. However, particles in QFT are not considered to be classical particles with definite positions and velocities. Scattering amplitudes, on the other hand, are quantities that describe the probabilities of particles undergoing scattering processes.