RENORMALIZABLE Meaning and
Definition
-
Renormalizable is an adjective that is primarily used in the field of theoretical physics, specifically in the context of quantum field theory. It refers to a property or characteristic of a theory or model where infinite quantities, such as divergent integrals or infinities arising in calculations, can be removed or canceled out by adjusting the parameters or inputs in a systematic and consistent manner.
In quantum field theory, the calculation of physical quantities often involves integrating over an infinite range of momenta. However, due to the inherent complexity of these calculations, infinities can arise that make the theory mathematically inconsistent. A renormalizable theory is one that can overcome this issue by introducing counter-terms, which are additional terms in the equations that cancel out the divergences.
Moreover, a renormalizable theory possesses the property that only a finite number of counter-terms are needed to remove the infinities at each perturbation order. This means that the theory remains mathematically well-defined and its predictions can be made accurately and sensibly. Renormalizability is a highly desirable feature for a physical theory since it ensures consistency and allows for meaningful predictions.
Overall, in the context of theoretical physics, the term "renormalizable" refers to a theory or model that successfully deals with infinities through the introduction of counter-terms, allowing for consistent calculations and predictions.
Etymology of RENORMALIZABLE
The word "renormalizable" is primarily used in the field of theoretical physics, specifically in the context of quantum field theory.
The term can be broken down into two parts: "re-" and "normalizable".
"Re-" is a prefix that means "repeating" or "again". It is commonly used to indicate repetition or restoration in various contexts.
"Normalizable" is derived from the word "normal", which in this case refers to mathematical functions that possess finite values. In quantum field theory, a "normalizable" function is one that can be integrated over all space without diverging to infinity. It implies that the function is well-behaved and can be meaningfully interpreted in the theory.
Putting it together, "renormalizable" implies a restoration or repetition of the capability of being normalizable.
