Gauge invariance ensures interactions are consistent from "summary" of The Quantum Theory of Fields by Steven Weinberg,Weinberg S
The concept of gauge invariance plays a crucial role in ensuring the consistency of interactions in quantum field theory. When we say that a theory is gauge invariant, we mean that the physical predictions of the theory remain unchanged under certain transformations known as gauge transformations. These transformations represent redundancies in the description of the theory, where different choices of the gauge may lead to equivalent physical results. In other words, gauge invariance implies that the theory is not dependent on the specific way we choose to describe it – the underlying physics remains the same regardless of the gauge we use. This property is essential for maintaining the consistency and predictability of the theory, as it ensures that physical observables are not affected by arbitrary choices made in the theoretical framework. By imposing gauge invariance, we impose constraints on the interactions allowed in the theory. These constraints serve to restrict the possible forms of interactions between the fundamental particles, ensuring that only physically meaningful processes are allowed. In this way, gauge invariance acts as a powerful tool for constraining the dynamics of the theory and removing unphysical degrees of freedom. Furthermore, gauge invariance has deep connections to the fundamental principles of quantum field theory, such as the conservation of electric charge and the principle of locality. The gauge symmetry of a theory is intimately related to the conservation laws that govern the interactions between particles, providing a unified framework for understanding the behavior of fundamental forces. In summary, gauge invariance is a fundamental principle that underlies the consistency and predictability of interactions in quantum field theory. By imposing constraints on the possible forms of interactions and ensuring that physical observables are independent of gauge choices, gauge invariance plays a crucial role in shaping the dynamics of the theory and connecting it to the underlying principles of quantum mechanics.
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