Ultravioletdivergenties

Ultravioletdivergenties are ultraviolet divergences that arise in quantum field theory when loop integrals over momenta extend to arbitrarily high energies, often due to short-distance contributions in Feynman diagrams. They appear in perturbative calculations across theories such as quantum electrodynamics, quantum chromodynamics, and various scalar field theories, as well as in some statistical field theories. The divergences are tied to the behavior of integrals at large momenta, reflecting sensitivity to physics at very short distances.

Regularization and renormalization are the standard techniques used to handle ultravioletdivergenties. Regularization introduces a temporary modification that makes the integrals finite, using methods such as a momentum cutoff, Pauli–Villars regulators, or dimensional regularization. Renormalization then absorbs the resulting infinities into redefined physical parameters—such as masses, coupling constants, and field normalizations—leaving finite, predictive results for observable quantities. In renormalizable theories, only a finite set of parameters requires adjustment.

In contemporary practice, ultravioletdivergenties are interpreted in several ways. In renormalizable theories, they signal the validity of the theory up to a certain energy scale. In effective field theories, the divergences are understood as a consequence of integrating out higher-energy degrees of freedom, with new physics expected to enter at higher scales. Lattice field theory provides a natural ultraviolet cutoff set by the lattice spacing. A UV-complete theory, such as a quantum theory of gravity, would ultimately resolve or supersede ultravioletdivergenties at the highest energies.