Physical Tuning and Naturalness

We present a radically new proposal for the solution of the naturalness/hierarchy problem, where the fine-tuning of the Higgs mass finds its physical explanation and the well-known multiplicative renormalization of the usual perturbative approach emerges as an IR property of the non-perturbative running of the mass.Comment: 7 pages, 4 figure

Dilution of zero point energies in the cosmological expansion

The vacuum fluctuations of all quantum fields filling the universe are supposed to leave enormous energy and pressure contributions which are incompatible with observations. It has been recently suggested that, when the effective nature of quantum field theories is properly taken into account, vacuum fluctuations behave as a relativistic gas rather than as a cosmological constant. Accordingly, zero-point energies are tremendously diluted by the universe expansion but provide an extra contribution to radiation energy. Ongoing and future cosmological observations could offer the opportunity to scrutinize this scenario. The presence of such additional contribution to radiation energy can be tested by using primordial nucleosynthesis bounds or measured on Cosmic Background Radiation anisotropy.Comment: 8 pages, no figures. Submitted the 17th of March to Modern Physics Letters

The Price of an Exact, Gauge-Invariant RG-Flow Equation

We combine old ideas about exact renormalization-group-flow (RGF) equations with the Vilkovisky-De Witt (VDW) approach to reparametrization invariant effective actions and arrive at a new, exact, gauge-invariant RGF equation. The price to be paid for such a result is that both the action and the RGF equation depend explicitly upon the base point (in field space) needed for the VDW construction. We briefly discuss the complications originating from this fact and possible ways to overcome them.Comment: 12 pages. To appear in Phys. Lett.

Comment on "Feynman Effective Classical Potential in the Schrodinger Formulation"

We comment on the paper "Feynman Effective Classical Potential in the Schrodinger Formulation"[Phys. Rev. Lett. 81, 3303 (1998)]. We show that the results in this paper about the time evolution of a wave packet in a double well potential can be properly explained by resorting to a variational principle for the effective action. A way to improve on these results is also discussed.Comment: 1 page, 2eps figures, Revte

Instability induced renormalization

It is pointed out that models with condensates have nontrivial renormalization group flow on the tree level. The infinitesimal form of the tree level renormalization group equation is obtained and solved numerically for the φ 4 model in the symmetry broken phase. We find an attractive infrared fixed point that eliminates the metastable region and reproduces the Maxwell construction. © 1999 Elsevier Science B.V. All rights reserved

Renormalization Group in Quantum Mechanics

We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of the well known pathologies which appear in quantum field theory due to the sharp cutoff. We show that for an arbitrary background path the usual local form of the action is not preserved by the flow. To cure this problem we consider a more general action than usual which is stable by the renormalization group flow. It allows us to obtain a new consistent renormalization group equation for the action.Comment: 20 page

Finite-momentum Bose-Einstein condensates in shaken 2D square optical lattices

We consider ultracold bosons in a 2D square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. It is therefore necessary to account for higher-order hopping terms, which are renormalized differently by the shaking, and introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates, with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott-insulator and the different superfluid phases, and present the time-of-flight images expected to be observed experimentally. Our results open up new possibilities for the realization of bosonic analogs of the FFLO phase describing inhomogeneous superconductivity.Comment: 7 pages, 7 figure

Effective action and the quantum equation of motion

We carefully analyse the use of the effective action in dynamical problems, in particular the conditions under which the equation \frac{\delta \Ga} {\delta \phi}=0 can be used as a quantum equation of motion, and the relation between the asymptotic states involved in the definition of \Ga and the initial state of the system. By considering the quantum mechanical example of a double-well potential, where we can get exact results for the time evolution of the system, we show that an approximation to the effective potential in the quantum equation of motion that correctly describes the dynamical evolution of the system is obtained with the help of the wilsonian RG equation (already at the lowest order of the derivative expansion), while the commonly used one-loop effective potential fails to reproduce the exact results.Comment: 28 pages, 13 figures. Revised version to appear in The European Physical Journal

Dark energy and Josephson junctions

It has been recently claimed that dark energy can be (and has been) observed in laboratory experiments by measuring the power spectrum $S_I(\omega)$ of the noise current in a resistively shunted Josephson junction and that in new dedicated experiments, which will soon test a higher frequency range, $S_I(\omega)$ should show a deviation from the linear rising observed in the lower frequency region because higher frequencies should not contribute to dark energy. Based on previous work on theoretical aspects of the fluctuation-dissipation theorem, we carefully investigate these issues and show that these claims are based on a misunderstanding of the physical origin of the spectral function $S_I(\omega)$. According to our analysis, dark energy has never been (and will never be) observed in Josephson junctions experiments. We also predict that no deviation from the linear rising behavior of $S_I(\omega)$ will be observed in forthcoming experiments. Our findings provide new (we believe definite) arguments which strongly support previous criticisms.Comment: 9 pages, no figure