User Tools

Site Tools


advanced_tools:renormalization:bphz

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Next revision
Previous revision
advanced_tools:renormalization:bphz [2017/09/26 16:24]
jakobadmin created
advanced_tools:renormalization:bphz [2018/05/05 12:33] (current)
jakobadmin ↷ Links adapted because of a move operation
Line 3: Line 3:
 <tabbox Why is it interesting?> ​ <tabbox Why is it interesting?> ​
  
-The Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme is an conceptually extremely interesting way to get rid of the infinities that arise in [[quantum_theory:​quantum_field_theory]]. In contrast to other popular scheme, the BPHZ method to get rid of infinites involves no UV cutoff. This is interesting,​ for example if one considers the famous hierarchy problem. Usually it is argued that a small mass for the Higgs particle is unnatural, because it gets loop corrections that are proportional to the cutoff squared. For a large cutoff scale like, for example, the Planck scale, one would therefore suspect a large Higgs mass, unless these corrections somehow cancel with the bare Higgs mass parameter. In the BPHZ scheme there is no cutoff and therefore no fine-tuning problem:+The Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme is an conceptually extremely interesting way to get rid of the infinities that arise in [[theories:​quantum_field_theory:canonical]]. In contrast to other popular scheme, the BPHZ method to get rid of infinites involves no UV cutoff. This is interesting,​ for example if one considers the famous hierarchy problem. Usually it is argued that a small mass for the Higgs particle is unnatural, because it gets loop corrections that are proportional to the cutoff ​$\Lambda$ ​squared
  
-<​blockquote>​It has been shown 5) that a different renormalization scheme (BPHZ) needs no fine tuning of the bare paramters.+$$m_H = m_0 + c \Lambda^2 + \ldots$$ 
 + 
 +For a large cutoff scale like, for example, the Planck scale, one would therefore suspect a large Higgs mass, unless these corrections somehow cancel with the bare Higgs mass parameter $m_0$. In the BPHZ scheme there is no cutoff and therefore no fine-tuning problem: 
 + 
 +<​blockquote>​It has been shown [[https://​inspirehep.net/​record/​12944?​ln=en|5)]] that a different renormalization scheme (BPHZ) needs no fine tuning of the bare paramters.
  <​cite>​[[https://​cds.cern.ch/​record/​143897/​files/​198304262.pdf|FINE-TUNING PROBLEM AND THE RENORMALIZATION GROUP]] by Wetterich</​cite></​blockquote>​  <​cite>​[[https://​cds.cern.ch/​record/​143897/​files/​198304262.pdf|FINE-TUNING PROBLEM AND THE RENORMALIZATION GROUP]] by Wetterich</​cite></​blockquote>​
  
Line 64: Line 68:
 </​tabbox>​ </​tabbox>​
  
 +{{tag>​theories:​quantum_theory:​quantum_field_theory}}
  
advanced_tools/renormalization/bphz.1506435881.txt.gz · Last modified: 2017/12/04 08:01 (external edit)