Why the electromagn potential obeys Callan-Symazik equa like Green Function?

In summary, the conversation discusses the relationship between the electromagnetic potential and the Callan-Symazik equation in renormalization group theory. It is suggested that the potential obeys the Callan-Symazik equation due to its similarity to propagator functions. The possibility of a relation between classical potential and interaction Hamiltonian is also mentioned. The concept of the Fourier transform of the electromagnetic potential is brought up, with the suggestion that it has a form similar to the scalar propagator. The relevance of the Callan-Symazik equation to both the Green function and the potential is explained, along with the idea that the potential undergoes similar variations under changing renormalization conditions. It is noted that the Callan equation does not
  • #1
ndung200790
519
0
Please teach me this:
Why the electromagnetic potential obeys the Callan-Symazik equation in renormalization group theory like propagator functions.By the way,are there any relation between classical potential and interaction Haminton(the product of different field operators).
Thank you very much in advance.
 
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  • #2
Now I think that the Fourier transform of electromagnetic potential has form of scalar propagator(because the potential in momentum space has form:1/square(momentum)).Then it must obey the Callan-Symazik equation like the Green function.Is that correct?
 
  • #3
At the moment,I think the Callan-Symazik describes the ''variable process'' under the change of renormalization condition with the ''terms'' that the Green function unchanging with bare parameter.The potential is also ''varied''similarly under changing renormalization.So it must be obeyed the Callan-Symazik like Green function
However,this Callan equation has not gamma function(relating with scale of fields in Green function case),because the potential is definite measurable,it does not shift from point to point of renormalization.Is that correct?
 

Related to Why the electromagn potential obeys Callan-Symazik equa like Green Function?

1. Why is the electromagn potential required to follow the Callan-Symazik equation?

The Callan-Symazik equation is a fundamental law in electromagnetism that describes the behavior of the electromagnetic potential. It is based on the principle of gauge invariance, which states that the physical laws of electromagnetism should not depend on the choice of gauge. Therefore, the electromagnet potential must obey the Callan-Symazik equation to maintain gauge invariance and ensure the consistency of the theory.

2. What is the significance of the Green Function in the Callan-Symazik equation?

The Green Function is a mathematical tool used to solve the Callan-Symazik equation. It represents the response of the electromagnetic potential to a point source, and it allows us to calculate the potential at any point in space. The Green Function is crucial in understanding the behavior of the electromagnetic potential and its relationship to the source of the field.

3. How does the Callan-Symazik equation relate to Maxwell's equations?

The Callan-Symazik equation is a direct consequence of Maxwell's equations, which are the fundamental equations of electromagnetism. Maxwell's equations describe how electric and magnetic fields are generated and how they interact with each other. The Callan-Symazik equation is a special case of Maxwell's equations that applies to the electromagnetic potential.

4. Can the Callan-Symazik equation be derived from first principles?

Yes, the Callan-Symazik equation can be derived from first principles using the principles of gauge invariance and the mathematical framework of quantum field theory. This equation is a result of many years of research and experimentation that has led to our current understanding of electromagnetism.

5. What are some practical applications of the Callan-Symazik equation?

The Callan-Symazik equation has various practical applications in fields such as electronics, telecommunications, and medical imaging. It is used to understand and manipulate electromagnetic fields, which are essential in the functioning of many modern technologies. Additionally, the Callan-Symazik equation has implications in the study of quantum mechanics and particle physics.

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