Renormalizability is important in two-dimensional space for QFT theories because it allows for the elimination of infinities that arise in calculations. This makes the theories more predictive and allows for better understanding of the underlying physical phenomena.
Renormalization is a mathematical technique used to remove infinities that arise in QFT theories. By removing these infinities, the theories become well-defined and can make accurate predictions about physical processes.
The dimensionality of space is a crucial factor in the renormalizability of QFT theories. In two-dimensional space, many theories become renormalizable due to the simpler mathematical structure, while in higher dimensions, the complexity of the calculations increases and renormalizability becomes more difficult to achieve.
No, not all QFT theories are renormalizable in two-dimensional space. While the simpler mathematical structure of two-dimensional space makes many theories renormalizable, there are still some theories that are not renormalizable even in two dimensions.
Yes, renormalizability can be achieved in higher dimensions for QFT theories, but it becomes increasingly difficult as the dimensionality increases. More complex mathematical techniques and approximations are needed to eliminate the infinities that arise in these higher dimensions.