Operational Dynamic Modeling

[Jimster41]

It seems like there are people working on dual formulations of fundamental interactions (dynamics, kinematics) all over the place: Quantum Spin Foams, Lattices, Energetic Causal Sets, Holographic Boundaries.

Wondering whether anyone can point toward theoretical research looking at fundamental particles and interactions using an "evolutionary dynamics" perspective. I've read a few things on evolutionary processes and I find myself repeatedly trying to analogize the Lagrangian as a "fitness" function, the operators as the player's DOF and rules, integrals of system evolution as the game trajectory over iteration, something to that effect, etc... Not having much luck finding stuff w/Google.

I did find this, which seemed to be addressing that general "kind" of approach but from assemblies of current Classical/QM pieces. Pretty cool though.

http://arxiv.org/abs/1105.4014

Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
Denys I. Bondar, Renan Cabrera, Robert R. Lompay, Misha Yu. Ivanov, Herschel A. Rabitz
(Submitted on 20 May 2011 (v1), last revised 29 Mar 2013 (this version, v5))
We introduce a general and systematic theoretical framework for Operational Dynamic Modeling (ODM) by combining a kinematic description of a model with the evolution of the dynamical average values. The kinematics includes the algebra of the observables and their defined averages. The evolution of the average values is drawn in the form of Ehrenfest-like theorems. We show that ODM is capable of encompassing wide ranging dynamics from classical non-relativistic mechanics to quantum field theory. The generality of ODM should provide a basis for formulating novel theories.

 

[AndyW]

Thank you for your interest in the topic of evolutionary dynamics in fundamental particle and interaction research. As a scientist in this field, I can point you towards some resources that may be helpful in your search.

Firstly, I would recommend looking into the field of quantum field theory, which is a theoretical framework that combines quantum mechanics with special relativity. This framework is widely used in particle physics and has been successful in describing many fundamental interactions. Within this framework, there are various approaches that incorporate evolutionary dynamics, such as the stochastic quantization method and the path integral formulation.

Additionally, there are ongoing research efforts in the field of quantum gravity, which seeks to unify general relativity with quantum mechanics. Many of these approaches also incorporate evolutionary dynamics in their models, such as loop quantum gravity and causal dynamical triangulations.

Furthermore, there are studies that explore the idea of emergent phenomena in fundamental interactions, where the behavior of particles and interactions can be described as an evolutionary process. This concept has been applied in various areas, such as quantum mechanics, statistical mechanics, and cosmology.

I hope these resources will be helpful in your search and provide you with a deeper understanding of evolutionary dynamics in fundamental particle and interaction research. Thank you for your interest and best of luck in your studies.