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waterfall
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Renormalization Group concept is rarely given in laymen book on QM and QFT and even Quantum Gravity book like Lisa Randall Warped Passages. They mostly described about
infinity minus infinity and left it from there. So if you were to write about QFT for Dummies. How would you share it such that common folks can understand them? I'll share what I know and some questions.
In the convensional popularization on the infinity problem, it is often said that:
M_correction = infinity
m_bare = m- infinity = - infinity
And in renormalization group, I understood it simply that instead of it, one simply assume m_bare is some definite value? Is that correct?
How about the M_correction. How did the value gets lower to finite?
But I went to many references. In the book The Story of Light. It was mentioned:
"With the bare mass also taken to be of infinite value, the two infinities - the infinities coming out of the perturbation calculations and the infinity of the bare mass - cancel each other out leaving us with a finite value for the actual, physical mass of an electron".
So as more detailed accounts or Renormalization. It is not just m_bare = m - infinity, but the perturbation calculation infinity minus the - m_bare = m_observed. Do you agree?
Now in Renormalization Group calculations. According to http://fds.oup.com/www.oup.co.uk/pdf/0-19-922719-5.pdf the fine structure constant for example is altered and this altered value is entered into the perturbation equation as well as mass and charge.. but how do you make a power series with an altered fine structure constant no longer diverge?? Landa pole is still landa pole whatever is the fine structure constant values.
Also someone said said "What's really happening is that your approximate theory is incomplete, and at some high energy, new physical processes show up, and change how the effective mass (charge, etc) varies with energy, so that the "bare" quantities are more reasonable.".
What is this example of new physical processes showing up at high energy that can affect or make effective mass varies with energy. I have a rough idea of Renormalization Group. Checked out many references for hours but want to get the essence and gist of it. I think this details of the nature of how new physical process showing up at high energy that can affect or make effective mass varies with energy (as well as fine structure constant varies with energy) can give the heart of the understanding.
Thanks.
infinity minus infinity and left it from there. So if you were to write about QFT for Dummies. How would you share it such that common folks can understand them? I'll share what I know and some questions.
In the convensional popularization on the infinity problem, it is often said that:
M_correction = infinity
m_bare = m- infinity = - infinity
And in renormalization group, I understood it simply that instead of it, one simply assume m_bare is some definite value? Is that correct?
How about the M_correction. How did the value gets lower to finite?
But I went to many references. In the book The Story of Light. It was mentioned:
"With the bare mass also taken to be of infinite value, the two infinities - the infinities coming out of the perturbation calculations and the infinity of the bare mass - cancel each other out leaving us with a finite value for the actual, physical mass of an electron".
So as more detailed accounts or Renormalization. It is not just m_bare = m - infinity, but the perturbation calculation infinity minus the - m_bare = m_observed. Do you agree?
Now in Renormalization Group calculations. According to http://fds.oup.com/www.oup.co.uk/pdf/0-19-922719-5.pdf the fine structure constant for example is altered and this altered value is entered into the perturbation equation as well as mass and charge.. but how do you make a power series with an altered fine structure constant no longer diverge?? Landa pole is still landa pole whatever is the fine structure constant values.
Also someone said said "What's really happening is that your approximate theory is incomplete, and at some high energy, new physical processes show up, and change how the effective mass (charge, etc) varies with energy, so that the "bare" quantities are more reasonable.".
What is this example of new physical processes showing up at high energy that can affect or make effective mass varies with energy. I have a rough idea of Renormalization Group. Checked out many references for hours but want to get the essence and gist of it. I think this details of the nature of how new physical process showing up at high energy that can affect or make effective mass varies with energy (as well as fine structure constant varies with energy) can give the heart of the understanding.
Thanks.
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