May 20, 2025
Scale dynamics in context: Connecting our framework to recent literature
Scale Dynamics in Context: Connecting Our Framework to Recent Literature
Scale Dynamics
Symplectic Geometry
Renormalization Group
Contact Geometry
Holographic RG
Read More
May 20, 2025
A scale Hamiltonian framework for multiscale systems: A Hamilton–Jacobi approach with application to glass-forming liquids
Abstract We develop a comprehensive scale Hamiltonian formalism for multiscale systems by recasting the renormalization group (RG) flow in a Hamiltonian framework and then reformulating it in terms of Hamilton–Jacobi...
renormalization group
glass transition
Hamiltonian
multiscale
physics
Read More
May 20, 2025
Irreversible scale dynamics: Contact geometry and the arrow of renormalization
In the post “From Time to Scale Dynamics” we treated scale evolution as perfectly conservative: a Hamiltonian $H_{\text{scale}}$ moved through symplectic phase‑space $(g_i,p_i)$ just like a planet through ordinary space....
Scale Dynamics
Renormalization Group
Contact Geometry
Entropy
C-theorem
Read More
May 20, 2025
Canonical transformations and scheme independence
Recap. In the post “From Time to Scale Dynamics” we traded the ordinary notion of time for the log‑scale $\tau = \ln(\mu/\mu_0)$ and promoted the Hamiltonian itself to the role of...
Scale Dynamics
Renormalization Group
Canonical Transformations
Hamiltonian Mechanics
Read More
May 20, 2025
Beyond the linear β: Higher-order scale dynamics — Revised
This post builds on “From Time to Scale Dynamics”, “Canonical Transformations & Scheme Independence”, and “Irreversible Scale Dynamics”. There we treated the renormalisation‑group (RG) β‑functions as the sole engine of...
Scale Dynamics
Renormalization Group
Nonlinear Flow
Hamiltonian Mechanics
Higher-Order Effects
Read More
May 15, 2025
From time to scale: A gentle introduction to scale dynamics
From time to scale: A gentle introduction to scale dynamics
Scale Dynamics
Renormalization Group
Hamiltonian Mechanics
Theoretical Physics
Quantum Field Theory
Read More
March 20, 2025
One more Copernican revolution: Reconsidering scale-centrism
One more Copernican revolution: reconsidering scale-centrism
Scale Relativity
Cosmology
Metaphysics
Copernican Principle
Multi-scale Universe
Read More