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samuelr85
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What I don't understand about WT identity is how it allows or helps you to renormalize a quantum field theory (es. QED). Not in details, just the basic ideas, if possible.
Thanks in advice
Thanks in advice
The Ward-Takahashi identity is a mathematical relationship between the correlation functions of a quantum field theory. It ensures that the theory is gauge invariant, meaning that the physical predictions of the theory do not depend on the choice of gauge. It is a fundamental principle in quantum field theory and plays a crucial role in understanding the behavior of particles and forces at the microscopic level.
The Ward-Takahashi identity is closely related to the process of renormalization in quantum field theory. Renormalization is a mathematical technique used to remove infinities that arise in certain calculations in quantum field theory. The Ward-Takahashi identity is used to ensure that the renormalization process preserves gauge invariance, which is essential for making meaningful predictions about the behavior of particles and forces.
The Ward-Takahashi identity is important because it is a fundamental principle that ensures the consistency and validity of quantum field theories. Gauge invariance is a crucial concept in modern physics and the Ward-Takahashi identity provides a powerful mathematical tool for understanding and maintaining gauge invariance in quantum field theories.
If the Ward-Takahashi identity is violated, it means that the theory does not possess gauge invariance. This can lead to inconsistencies and inaccuracies in the theory's predictions about the behavior of particles and forces. Violation of the Ward-Takahashi identity can also indicate a fundamental flaw in the underlying principles of the theory, which would require further investigation and refinement.
The Ward-Takahashi identity is a purely mathematical relationship between correlation functions, so it cannot be directly tested in experiments. However, it is an essential part of the theoretical framework of quantum field theory and its predictions have been extensively tested and verified through experimental observations in particle accelerators and other high-energy experiments. Any violations of the Ward-Takahashi identity would be reflected in discrepancies between the theoretical predictions and experimental results.