Renormalization is a powerful technique used in quantum field theory (QFT) to address the issue of infinities that arise in calculations of particle interactions. In QFT, particles and their interactions are described by fields that are quantized, meaning they are described in terms of creation and annihilation operators. However, when performing calculations using these quantum fields, infinities can arise in certain calculations, such as loop diagrams.
The infinities arise due to the presence of divergent integrals in these loop diagrams, where momentum integrals extend to arbitrarily large values. These divergences indicate that the theory is not well-defined at the quantum level and needs to be properly regulated and renormalized.
Renormalization involves a systematic procedure to absorb these infinities into the definition of certain physical quantities, such as mass and charge, in a way that maintains the predictive power of the theory. The goal is to obtain finite and meaningful results that can be compared to experimental observations.
There are mainly two types of renormalization techniques used in QFT: regularization and renormalization itself.
Regularization: Regularization is the first step in the renormalization procedure. It involves introducing a regularization parameter or a cutoff that serves to regulate the divergences in the calculations. The cutoff effectively limits the range of momenta that contribute to the loop integrals, preventing them from reaching infinitely large values. Various regularization schemes can be employed, such as dimensional regularization or momentum space cutoffs.
Renormalization: Once the divergences are regulated, the renormalization procedure aims to remove these infinities and redefine the theory in a consistent way. This involves introducing counterterms, which are additional terms in the Lagrangian or the equations of motion, that cancel out the divergent contributions from the loop diagrams.
The counterterms contain parameters, often called coupling constants or bare parameters, that are initially introduced as arbitrary values. These parameters are then adjusted such that the physical observables, such as particle masses and charges, match the experimental measurements. This process is usually done by imposing certain renormalization conditions, where the values of the parameters are fixed by experimental data.
By employing regularization and renormalization, the infinities arising in the calculations are absorbed into the redefined parameters of the theory, resulting in finite and meaningful predictions for physical observables. The renormalized theory can then be used to make precise predictions that can be compared to experimental results, providing a consistent and successful framework for understanding particle interactions.