Centre de Physique Théorique


Vendredi 1er décembre 2017

11h00 – 12h00, Amphi 5 du CPT

Wavelets and renormalization group in quantum field theory

M.V. Altaisky, Small Space Research Institute RAS, Moscow, Russia.


The method of continuous wavelet transform in quantum field theory, presented in
[1, 2, 3], consists in substitution of the local fields $\phi(x)$ by those dependent on both the position $x$ and the resolution $a$.
The substitution of the action $S[\phi(x)]$ by the action $\tilde S[\phi_a(x)]$,
where $\phi_a(x)$ is wavelet transform of $\phi(x)$, results in quantum field theory models finite by construction, if causality conditions are applied in the
scale variable $a$. The renormalization group is shown to be symmetry group of the
theory $\tilde S[\phi_a(x)]$. The space of
scale-dependent functions ${ \phi_a(x) }$ is more relevant to physical reality than
the space of square-integrable functions $L^2(\mathbb R^d)$, since what is really measured in any experiment is
always defined in a region rather than point. The effective action $\Gamma_a$ of our theory turns to be complementary to
the exact renormalization group effective action, since the former includes the fluctuations of all scales, from large IR scales to the UV scale of observation $a$ [4]. The standard renormalization group results for $\phi^4$ model are reproduced. Examples from QED, QCD
and turbulence theory are presented.

M. V. Altaisky.
\newblock Wavelet based regularization for Euclidean field theory.
\newblock \em IOP Conf. Ser., 173:893—897, 2003.

M. V. Altaisky.
\newblock Quantum field theory without divergences.
\newblock \em Phys. Rev. D, 81:125003, 2010.

M. V. Altaisky and N. E. Kaputkina.
\newblock Continuous wavelet transform in quantum field theory.
\newblock \em Phys. Rev. D, 88:025015, 2013.

M. V. Altaisky.
\newblock Unifying renormalization group and the continuous wavelet transform.
\newblock \em Phys. Rev. D, 93:105043, 2016.