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Qmechanic ♦
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What is the meaning of the variables in the Lagrangian before renormalization?

fix a few typos
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Amit
Amit
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I'm currently working through Coleman's lectures on Quantum field theory qndand I cannot quite get my head around the whole concept of renormalization.

What I am aware of, is that you have some Lagrangian and you want to impose some normalization conditions on the fields (e.g. $< 0|\phi(0)|0>=0$). Since this cannot be satisfied as is, the Lagrangian has to be split up into a physical part which contains all terms with the physical variables (e.g. the physical masses, the physical coupling constant), and a part which contains counterterms. These can then be chosen such as to satisfy the needed normalization conditions.

Here is now my question: What is the interpretation of the variables, like masses and coupling constants, before the splitting of the Lagrangian? I don't quite get why they souldshould not be already the physical quantities, since if for example I have a classical Lagrangian for a harmonic oscillator, the mass and frequency appearing there are simply the physical mass and the physical frequency. Why is it different in QFT? And what is the precise meaning of the variables before renormalization?

I'm currently working through Coleman's lectures on Quantum field theory qnd I cannot quite get my head around the whole concept of renormalization.

What I am aware of, is that you have some Lagrangian and you want to impose some normalization conditions on the fields (e.g. $< 0|\phi(0)|0>=0$). Since this cannot be satisfied as is, the Lagrangian has to be split up into a physical part which contains all terms with the physical variables (e.g. the physical masses, the physical coupling constant), and a part which contains counterterms. These can then be chosen such as to satisfy the needed normalization conditions.

Here is now my question: What is the interpretation of the variables, like masses and coupling constants, before the splitting of the Lagrangian? I don't quite get why they sould not be already the physical quantities, since if for example I have a classical Lagrangian for a harmonic oscillator, the mass and frequency appearing there are simply the physical mass and the physical frequency. Why is it different in QFT? And what is the precise meaning of the variables before renormalization?

I'm currently working through Coleman's lectures on Quantum field theory and I cannot quite get my head around the whole concept of renormalization.

What I am aware of, is that you have some Lagrangian and you want to impose some normalization conditions on the fields (e.g. $< 0|\phi(0)|0>=0$). Since this cannot be satisfied as is, the Lagrangian has to be split up into a physical part which contains all terms with the physical variables (e.g. the physical masses, the physical coupling constant), and a part which contains counterterms. These can then be chosen such as to satisfy the needed normalization conditions.

Here is now my question: What is the interpretation of the variables, like masses and coupling constants, before the splitting of the Lagrangian? I don't quite get why they should not be already the physical quantities, since if for example I have a classical Lagrangian for a harmonic oscillator, the mass and frequency appearing there are simply the physical mass and the physical frequency. Why is it different in QFT? And what is the precise meaning of the variables before renormalization?

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Armando Hauser
Armando Hauser
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What is the meaning of the variables in the Lagrangian before renormalization

I'm currently working through Coleman's lectures on Quantum field theory qnd I cannot quite get my head around the whole concept of renormalization.

What I am aware of, is that you have some Lagrangian and you want to impose some normalization conditions on the fields (e.g. $< 0|\phi(0)|0>=0$). Since this cannot be satisfied as is, the Lagrangian has to be split up into a physical part which contains all terms with the physical variables (e.g. the physical masses, the physical coupling constant), and a part which contains counterterms. These can then be chosen such as to satisfy the needed normalization conditions.

Here is now my question: What is the interpretation of the variables, like masses and coupling constants, before the splitting of the Lagrangian? I don't quite get why they sould not be already the physical quantities, since if for example I have a classical Lagrangian for a harmonic oscillator, the mass and frequency appearing there are simply the physical mass and the physical frequency. Why is it different in QFT? And what is the precise meaning of the variables before renormalization?