Centre de Physique Théorique


Friday 1 December 2017

11h00 – 12h00, CPT, Amphi 5

Wavelets and renormalization group in quantum field theory

Mikhail Altaisky (Centre de Recherches spatiales, Moscou)


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.

14h00 – 15h00, CPT, Amphi 5

Space-time discreteness in quantum gravity: possible consequences and a new perspective on the origin of dark energy 

Alejandro Perez

In this seminar I will first quickly review the results of the canonical quantization of general relativity suggesting a fundamentally discrete nature of geometry at the Planck scale. This calls for a fundamental description that is combinatorial and discrete where the smooth spacetime description of QFT and general relativity would only be emergent from the collective behavior of the Planckian local structures. In this framework time and Lorentz invariance are still open issues. Nevertheless, discreteness helps, as we will discuss, understanding some of the enigmatic properties of semiclassical black holes: it clarifies the origin of black hole entropy and provides a natural perspective on the issue of information in black hole evaporation.

A natural consequence of the hypothesis that the smooth spacetime description is emergent is, I will argue in the second part, the possibility of energy diffusion from low energy degrees of freedom (effectively described by general relativity coupled to matter fields) to the underlying Planckian micro structure at the fundamental level. I will show that, in the context of cosmology, such effect leads to a novel perspective on the origin of dark energy. A phenomenological model that yields interesting quantitative estimates will be presented.