A renormalizable theory is a theory that can be used to describe physical phenomena at different scales without encountering infinite or non-physical results. It is a theoretical framework that allows for the mathematical treatment of divergent quantities in a way that still produces meaningful and accurate results.
A theory is considered renormalizable if the divergent quantities in its mathematical equations can be absorbed into a finite number of parameters. This process is known as renormalization and involves making changes to the theory's parameters in order to account for the effects of very small or very large scales.
A renormalizable theory is significant because it allows for the prediction of physical phenomena at different scales, from the very small to the very large. It also allows for the calculation of physical quantities with high precision, making it a useful tool in theoretical physics and particle physics.
No, not all theories can be renormalized. Some theories, such as those that involve gravity, cannot be renormalized because they lead to infinite or non-physical results that cannot be absorbed into a finite number of parameters.
The concept of renormalizability is important in the search for a theory of everything because it allows for the merging of different theories at different scales. A theory of everything must be able to accurately describe physical phenomena at all scales, and the ability to renormalize a theory is a key aspect in achieving this goal.