Hamiltonian Dynamics in Fundamental Physics
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".
Deadline for manuscript submissions: 30 June 2026 | Viewed by 15
Special Issue Editor
2. Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel
3. Department of Physics, Ariel University, Ariel 40700, Israel
Interests: relativistic quantum mechanics and quantum field theory; theory of classical and quantum unstable systems and chaos; quantum theory on hypercomplex Hilbert modules; complex projective spaces in quantum dynamics; relativistic statistical mechanics and thermodynamics; high-energy nuclear structure and particle physics
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Special Issue Information
Dear Colleagues,
Hamiltonian dynamics provides a profound and unifying framework for describing the evolution of physical systems, from classical point particles to relativistic fields and quantum states. Its principles, centered on phase space structure, symplectic geometry, and conservation laws, are the bedrock of modern theoretical physics. This formalism is not only essential for analyzing integrability, chaos, and stability but also serves as the critical pathway towards quantization, bridging the classical and quantum worlds through canonical methods.
In contemporary fundamental physics, the application of Hamiltonian dynamics is pushing the boundaries of our understanding in diverse and profound areas. A particularly rich avenue of research concerns Hamiltonians of the form pgp (with tensor indices), which naturally generate, via the Hamilton equations, a dynamical manifold with g as the metric. The evolution of such geometric structures—whether driven by intrinsic curvature-driven flows such as the Ricci flow or by other physical perturbations—offers fertile ground for exploration. The study of these evolving manifolds, including questions of their convergence, stability, and singularity formation, is of significant mathematical and physical interest, linking fundamental physics to geometric analysis.
This Special Issue aims to highlight recent advancements and foster new research at the intersection of Hamiltonian dynamics and the core problems of fundamental physics. We seek contributions that explore both the formal development of the Hamiltonian framework and its cutting-edge applications. We also welcome reviews offering a synthesis of recent progress.
Topics of interest include, but are not limited to, the following:
- Canonical General Relativity and Quantum Gravity: Constraint analysis, ADM formalism, Ashtekar variables, and applications in loop quantum gravity or spin foams.
- Hamiltonian Formulations of Gauge Theories: Canonical quantization, BRST formalism, and topological field theories.
- Gravitational Waves and Binary Dynamics: Hamiltonian methods for post-Newtonian and post-Minkowskian calculations, effective-one-body formalism, and chaos in N-body systems.
- Geometric Flows and Hamiltonian Dynamics: Ricci flow and other curvature flows as generated by Hamiltonian systems; stability and convergence properties of geometrically evolving manifolds.
- Cosmological Perturbation Theory: Hamiltonian approaches to the evolution of scalar and tensor perturbations and quantum-to-classical transition.
- Integrability and Chaos: Classical and quantum chaos in gravitational systems, out-of-time-order correlators (OTOCs), and the Kolmogorov–Arnold–Moser (KAM) theory in fundamental contexts.
- Symplectic Geometry and Geometric Quantization: Advanced mathematical foundations and their physical implications.
- Statistical Mechanics and Thermodynamics of Gravity: Black hole thermodynamics, the concept of entropy in isolated gravitational systems, and the connection to information theory.
This Special Issue of Entropy aims to compile original research and review articles that explore the central role of Hamiltonian dynamics in addressing the most pressing questions in fundamental physics, gravitation, and cosmology.
Prof. Dr. Lawrence Horwitz
Guest Editor
Manuscript Submission Information
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Keywords
- Hamiltonian dynamics
- canonical quantization
- general relativity
- symplectic geometry
- quantum gravity
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