mhill said:Given a theory with n-different fields [tex] \phi _{n}(x) [/tex] and a known Lagrangian L is possible to see at first sight if the theory will be renormalizable or non*-renormalizable ?? , or on the other hand should we calculate ALL the infinite diagramms to see it, for example i give a certain Lagrangian involving scalar particles, spin 1 particles and spin*-2 particles and several coupling constants could you say if this is renormalizable or not ?
lbrits said:There are general theorems based on power counting which tell you which theories are NOT renormalizable. You end up with so few remaining that you can just go around testing them one by one, I believe. I think it is pretty well discussed in Peskin and Schroeder.
Renormalizability is a concept in theoretical physics that refers to the ability of a theory to produce finite and meaningful results when calculating physical quantities. In simpler terms, it is the property of a theory to be able to account for all the relevant interactions and produce predictions that are not infinitely large or undefined.
To determine if a theory is renormalizable, one must analyze its mathematical structure and look for potential divergences, or infinite values, in the equations. If these divergences are present, the theory is considered non-renormalizable. However, if the divergences can be removed through a process called renormalization, the theory is deemed renormalizable.
Renormalizability is crucial in theoretical physics because it ensures that a theory is well-defined and can make accurate predictions about the physical world. Non-renormalizable theories often lead to nonsensical or unphysical results, making them unreliable for describing the universe.
Yes, a non-renormalizable theory can still be useful in certain contexts. While it may not accurately describe all physical phenomena, it can still provide insight and make predictions in limited situations. Non-renormalizable theories are also often used as low-energy approximations of more fundamental theories.
No, not all physical theories are renormalizable. In fact, many theories, such as general relativity, are non-renormalizable. This is because they involve infinitely many parameters and interactions, making it impossible to remove all divergences through renormalization. However, renormalizable theories are preferred as they are more mathematically elegant and reliable in predicting physical phenomena.