Oui la découverte du boson de Higgs pourrait bien être aussi importante pour l'histoire de la pensée humaine que la loi de la gravitation universelle de Newton
If we could establish a Coleman-Weinberg origin of the Higgs boson mass, we would then have two scales in nature generated by quantum loop effects: ΛQCD and vweak. The grand hypothesis that: “all mass in nature comes from quantum mechanics” would gain signiﬁcant validation. Our view of the UV would then have to accomodate it. This hypothesis may ultimately imply a radically different view of nature than our current “Grand Unified Theories to strings” philosophy. Some of these issues and “predictions” have been discussed elsewhere . For example, we live in a D=4 universe, and it is striking that D=4 is the only possibility for classical scale symmetry given Yang-Mills ﬁeld theories as an underpinning of nature, since the trace of the Yang-Mills ﬁeld stress tensor is classically zero only in D=4. Quantum mechanics then supplies the trace anomaly and allows for the generation of mass and large hierarchies through the renormalization group. We see this with QCD and the compelling question is whether it also applies to the weak scale and Higgs boson. Hence, the hypothesis that “all mass in nature comes from quantum mechanics” already seems broadly consistent with our D=4, large universe. The stakes are high: this may ultimately require a classically scale-invariant approach to gravity, such as D=4 Weyl gravity with a quantum, QCD-like origin of MPlanck  (see also  and references therein).
Christopher T. Hill, 27 janv 2014
In this note we will show the intimate relationships between Weyl anomalies, the dilaton and the Higgs ﬁeld in the framework of spectral physics. The framework is the expression of a ﬁeld theory in terms of the spectral properties of a (generalized) Dirac operator. In this respect this work can be seen in the framework of the noncommutative geometry approach to the standard model of Connes and collaborators [1, 2, 3, 4], as well as of Sakharov induced gravity  (for a modern review see )... It is known, and this is the essence of the noncommutative geometry approach to the standard model, that the theory is described by a fermionic action and a bosonic action, both of which can be expressed in terms of the spectrum of the Dirac operator. In  two of us have shown that if one starts from the classic fermionic action and proceeds to quantize the theory with a regularization based on the spectrum, an anomaly appears. it is possible that the full quantum theory is still invariant by correcting the path integral measure. This is tantamount to the addition of a term to the action, which renders the bosonic background interacting to the dilaton ﬁeld. The main result of that paper is that this term is a modiﬁcation of the bosonic spectral action . In this case the theory is still invariant. In this paper we have a shift of the point of view. We still consider the theory to be regularized in the presence of a cutoff scale, but we consider this scale to have a physical meaning, that of the breaking of Weyl invariance. We then consider the ﬂow of the theory at a renormalization scale, which is not necessarily the scale which breaks the invariance. The theory has a dilaton, and the Higgs ﬁeld. The dilaton may involve a collective scalar mode of all fermions accumulated in a Weyl-noninvariant dilaton action. Accordingly the spectral action arises as a part of the fermion eﬀective action divided into the Weyl non-invariant and Weyl invariant parts. We calculate the dilaton eﬀective potential and we discuss how it relates to the transition from the radiation phase with zero vacuum expectation value of Higgs ﬁelds and massless particles to the electroweak broken phase via condensation of Higgs ﬁelds. The collective ﬁeld of dilaton can provide the above mentioned phase transition with EW symmetry breaking during the evolution of the universe.
A.A. Andrianov, M.A. Kurkov, Fedele Lizzi, 2011
(*Ce billet est dédicacé à Stéphane B. en particulier et plus généralement à tous mes collègues du jeudi...;-)
//Un mot a été remplacé par un autre le 15 décembre 2015.