Field equations govern particle behavior from "summary" of The Quantum Theory of Fields by Steven Weinberg,Weinberg S
The behavior of particles in the quantum theory of fields is governed by field equations. These equations describe how fields change and evolve in space and time. The interactions between particles are mediated by these fields, which act as carriers of force between them. In this framework, particles are considered excitations of the underlying fields. When a particle is created or destroyed, it is the field that undergoes a corresponding change. The field equations dictate how these changes occur and how particles move and interact with each other. The field equations are derived from the principles of quantum mechanics and special relativity. They are formulated in a way that is consistent with both theories and provide a unified description of particle behavior at the quantum level. By solving these field equations, one can predict the behavior of particles in different physical scenarios. The equations allow us to calculate the probabilities of different outcomes in particle interactions and to understand the underlying mechanisms at work.- The concept that field equations govern particle behavior is fundamental to the quantum theory of fields. It provides a mathematical framework for describing the dynamics of particles and their interactions, allowing us to make precise predictions and deepen our understanding of the quantum world.
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