- #1
copernicus1
- 99
- 0
Can you look at an interaction term in your lagrangian or hamiltonian, like L_{\rm int} or H_{\rm int}, and say immediately how its diagrams will diverge (as in quartic, quadratic, linear, log, etc.)?
There are three main types of divergences for a given interaction: UV (ultraviolet), IR (infrared), and Logarithmic. UV divergences arise when the energy of a particle becomes very high, causing the interaction to become infinite. IR divergences occur when the energy of a particle becomes very low, leading to a similar infinite behavior. Logarithmic divergences arise when the energy is neither too high nor too low, but rather at an intermediate scale.
The presence of divergences in a given interaction can make it difficult to accurately describe and predict the behavior of particles involved. They can also cause theoretical predictions to become infinite, making it necessary to use mathematical techniques such as renormalization to remove these divergences and obtain meaningful results.
While some interactions may naturally produce divergences, it is possible to avoid them by choosing specific values for the parameters involved in the interaction. This is known as fine-tuning and can be used to eliminate or reduce the effects of divergences.
To deal with divergences in calculations, scientists use techniques such as dimensional regularization and renormalization. These methods involve redefining the parameters involved in the interaction to eliminate or reduce the effects of divergences. This allows for more accurate predictions and descriptions of the interaction.
Divergences play a crucial role in the development of new theories in physics. By studying the divergences that arise in different interactions, scientists can gain insights into the underlying principles and mechanisms at work. This can lead to the development of new theories and models that better describe and predict the behavior of particles and interactions.