Related papers: Estimating quantities conserved by virtue of scale…
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a…
Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the…
Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
Scale invariance supplemented by the requirement of the absence of new heavy particles may play an important role in addressing the hierarchy problem. We discuss how the Standard Model may become scale invariant at the quantum level above a…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
Lagrangian modelling can be used to derive mathematical models for complex power electronic converters. This approach uses scalar quantities (kinetic and potential energy) to derive models, which is simpler than using (vector-based) force…
This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions; namely, the coupling of the order-parameter fluctuations to other soft modes, and the resulting impossibility of…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…
A generalised form of time-translation-invariance permits to re-derive the known generic phenomenology of ageing, which arises in classical many-body systems after a quench from an initially disordered system to a temperature $T\leq T_c$,…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and…
On the basis of dynamical principles we derive the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and demonstrate that scale-invariance and a mean-value constraint are…
The scalar normal modes of higher dimensional gravitating kink solutions are derived. By perturbing to second order the gravity and matter parts of the action in the background of a five-dimensional kink, the effective Lagrangian of the…
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces has been proposed. This single postulate replaces the assumptions on…
We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from order (regularity) to disorder (chaos). The systems are described by a two-dimensional, nonlinear mapping that preserves the area in…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
We consider the application of the theory of symmetries of coupled ordinary differential equations to the case of reparametrisation invariant Lagrangians quadratic in the velocities; such Lagrangians encompass all minisuperspace models. We…