In quantum field theory (QFT), particles are not considered to be fundamental entities with well-defined positions or sizes in the same way as classical objects. Instead, particles are described as excitations or quanta of the underlying quantum fields.
When researchers speak about the size of particles in QFT, they are often referring to the concept of the particle's "compton wavelength." The Compton wavelength is a fundamental property associated with a particle and is related to its momentum. It characterizes the scale over which a particle's wave-like properties become significant.
The Compton wavelength is derived from the quantum mechanical principles of wave-particle duality. It relates the momentum of a particle to the wavelength of its associated wave. In simple terms, it indicates the spatial extent over which a particle's quantum behavior is manifest.
However, it's important to note that the Compton wavelength should not be interpreted as the "size" of a particle in the classical sense. It does not imply that the particle is a tiny object with a specific boundary or extent. Rather, it signifies the characteristic scale at which a particle's wave-like nature becomes noticeable.
In practice, the Compton wavelength is often used to estimate the spatial resolution required to probe a particle's properties experimentally. For instance, in high-energy physics experiments, researchers may employ particle accelerators with energies corresponding to length scales comparable to the Compton wavelength of the particles they wish to investigate.
It's worth emphasizing that the description of particles in QFT is deeply rooted in the framework of quantum mechanics, where the concept of precise position and size loses its classical meaning. Instead, the properties of particles are defined in terms of their interactions with quantum fields and the probabilities of various measurement outcomes.