These regularized integrals depend on parameters such as the momentum cut-off, the Pauli-Villars masses, and the dimensional regularization
parameter, which are used in the corresponding regularization procedure.
Since the expectation value <[[phi].sup.2]> diverges, we regularize it using the dimensional regularization method:
We have discussed the dimensional regularization approach to the renormalization group theory of the generalized sine-Gordon model.
The areas they cover here are quantum mechanics (revisited) angular momentum, scattering theory, Lagrangian field theory, symmetries, quantum electrodynamics, higher-order processes, path integrals, the multi-pole analysis of the radiation field, irreducible representations of SU(n), Lorentz transformation in quantum field theory, and dimensional regularization
. ([umlaut] Ringgold, Inc., Portland, OR)
Nevertheless, such a precise calculation is on the basis of some regularization methods, for example, dimensional regularization
Their tool, known as dimensional regularization
and first described in 1971, also applies to similar theories that describe other forces.
This leads to the problem with convergence of chiral series, and it can be solved using some kind of cutoff regularization instead of common dimensional regularization scheme.
Dimensional regularization scheme is not particularly suitable for effective field theories since it gets large contributions from short distance physics .