The purpose of exploring free and interaction terms of L in quantum field theory is to understand the behavior of particles and their interactions at the microscopic level. The free terms describe the particles and their properties in the absence of interactions, while the interaction terms describe how particles interact with each other and exchange energy and momentum.
In quantum field theory, the free and interaction terms are related through the Lagrangian density, which is a mathematical expression that describes the dynamics of a quantum field. The free terms are typically quadratic in the field operators, while the interaction terms are higher-order terms that involve products of field operators.
The coupling constant in the interaction terms of L represents the strength of the interaction between particles. It determines the probability of particles interacting with each other and the strength of the resulting interaction. In some cases, the coupling constant may also depend on the energy of the particles involved.
The free terms determine the properties and behavior of individual particles, such as their mass and spin. The interaction terms, on the other hand, govern how particles interact with each other and can lead to phenomena such as particle scattering and particle creation and annihilation. Together, these terms determine the overall behavior and evolution of a quantum field system.
Yes, free and interaction terms can be modified or added in quantum field theory. This is often done to incorporate new interactions or particles into the theory, or to improve its predictive power. However, any modifications or additions must still be consistent with the principles and equations of quantum field theory to ensure the validity of the theory.