Related papers: Fiducial Symmetry in Action
We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and…
In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously…
The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…
In this work, a novel mechanism for spontaneous symmetry breaking is presented. This mechanism avoids quadratic divergencies and is thus capable of addressing the hierarchy problem in gauge theories. Using the scale-dependent effective…
The possibility of mass in the context of scale-invariant, generally covariant theories, is discussed. Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form $S…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
The discovery of the scalar boson completes the experimental confirmation of the particles predicted by the Standard Model, which achieves to describe almost all phenomena observed in nature in terms of a few symmetry principles and a…
How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…
A robust prediction model invoking the Takens embedding theorem, whose \textit{working hypothesis} is obtained via an inference procedure based on the minimum Fisher information principle, is presented. The coefficients of the ansatz,…
Supersymmetry plays a fundamental role in the radiative stability of many inflationary models. Spontaneous breaking of the symmetry inevitably leads to fields with masses of order the Hubble scale during inflation. When these fields couple…
Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-consistent dimensional scalings. Here, we express this…
Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and inference that puzzled our founding fathers remain unanswered. To…
Consistency relations -- which relate an N-point function to a squeezed (N+1)-point function -- are useful in large scale structure (LSS) because of their non-perturbative nature: they hold even if the N-point function is deep in the…
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental…
The fidelity (Shannon mutual information between measurements and physical quantities) is proposed as a quantitative measure of the quality of physical measurements. The fidelity does not depend on the true value of unknown physical…
Accidental symmetries in effective field theories can be established by computing and comparing Hilbert series. This invites us to study them with the tools of invariant theory. Applying this technology, we spotlight three classes of…
The great power of EQuilibrium (EQ) statistical physics comes from its principled foundations: its First Law (conservation), Second Law (variational tendency principle), and its Legendre Transforms from observables $(U, V, N)$ to their…
The recently discovered conserved quantity associated with Kepler rescaling is generalised by an extension of Noether's theorem which involves the classical action integral as an additional term. For a free particle the familiar…