Renormalisaatioryhmäajatus

Renormalisation is a technique used in quantum field theory and statistical mechanics to handle infinities that arise in calculations. When physical quantities like energy or mass are calculated using perturbation theory, integrals often diverge, leading to infinite results. Renormalisation provides a systematic way to manage these infinities and extract meaningful, finite predictions.

The core idea is that the "bare" parameters of a theory, such as mass and charge, are not directly observable. Instead, what we measure are "renormalised" parameters that include the effects of interactions with quantum fluctuations. These interactions effectively dress the bare particles, altering their properties.

The process typically involves introducing a cutoff, a limit on the energies or momenta considered, to make the integrals finite. Then, the divergent parts of the calculated quantities are absorbed into redefinitions of the original parameters. These redefinitions are chosen such that the physical observables remain finite and independent of the cutoff.

Different renormalisation schemes exist, such as dimensional regularisation or Pauli-Villars regularisation, each with its own advantages. The consistency of the theory is preserved through the Renormalisation Group, which describes how the parameters of the theory change with the energy scale at which they are measured. This scale dependence is a crucial aspect of modern physics, particularly in understanding phenomena like asymptotic freedom in quantum chromodynamics. Ultimately, renormalisation allows quantum field theories to make precise, testable predictions about the physical world.