Renormalizability is a property of a quantum field theory that allows for the absorption of infinities arising from loop diagrams into a finite number of redefined (renormalized) parameters, such as masses and coupling constants. A renormalizable theory ensures that predictions remain finite and physically meaningful after renormalization.
Triple and quadruple vertices correspond to interaction terms involving three or four fields, respectively, in the Lagrangian of a quantum field theory. These vertices are crucial because they determine the types of interactions that particles can undergo, influence the structure of Feynman diagrams, and affect the renormalizability of the theory.
Triple and quadruple vertices can affect the renormalizability of a theory by introducing interaction terms that may lead to divergences in loop diagrams. The power-counting of these vertices helps determine whether the divergences can be absorbed into a finite number of renormalized parameters. For a theory to be renormalizable, the vertices must lead to divergences that can be systematically controlled.
Power-counting is a method used to analyze the degree of divergence of Feynman diagrams based on the dimensions of the fields and coupling constants involved in the vertices. By examining the superficial degree of divergence, power-counting helps determine whether the infinities arising in the theory can be renormalized. A theory is renormalizable if the divergences can be absorbed by a finite number of counterterms.
Yes, non-renormalizable theories can still be useful as effective field theories, which are valid at a certain energy scale. While they may not be renormalizable in the traditional sense, they can provide accurate descriptions of physical phenomena within their domain of applicability. At higher energies, these theories are expected to be replaced by a more fundamental, renormalizable theory.