Mathematical Physics (MTP)

Section Information

Mathematical Physics focuses on the application of mathematical methods to understand physical phenomena and develop theoretical frameworks that support modern physics. It bridges rigorous mathematics with fundamental and applied areas of physics, providing tools for modeling, analysis, and prediction.

Modern research in mathematical physics includes quantum mechanics, statistical physics, relativity, field theory, spectral theory, nonlinear dynamics, and partial differential equations. Advances in geometry, topology, operator theory, and computational methods continue to deepen the understanding of physical laws.

This section publishes theoretical studies, analytical developments, mathematical models, computational approaches, and interdisciplinary research that explore the mathematical foundation of physical systems and contribute to advancements in theoretical and applied physics.

Scope

Quantum Mechanics and Quantum Theory
- Mathematical structure of quantum systems
- Spectral theory, operator algebras, and Hilbert space methods
- Quantum dynamics, scattering theory, and perturbation theory
- Foundations of quantum mechanics and quantum information
Statistical and Thermal Physics
- Statistical ensembles, thermodynamic limits, and phase transitions
- Stochastic processes and probabilistic methods
- Non-equilibrium systems and fluctuation phenomena
- Mathematical models of complex and disordered systems
Classical and Quantum Field Theory
- Gauge theory, symmetries, and variational principles
- Renormalization, path integrals, and functional methods
- Topological field theories and geometric formulations
- Applications in particle physics, cosmology, and condensed matter
General Relativity and Gravitation
- Mathematical structure of spacetime and curvature
- Einstein field equations and exact solutions
- Black holes, gravitational waves, and cosmological models
- Differential geometry and geometric analysis in relativity
Differential Equations in Physics
- Ordinary and partial differential equations arising in physics
- Nonlinear waves, solitons, and integrable systems
- Reaction–diffusion systems and physical modeling
- Analytical and numerical solution methods
Dynamical Systems and Chaos
- Stability, bifurcation theory, and long-term behavior
- Chaotic systems and deterministic complexity
- Hamiltonian and symplectic dynamics
- Applications in celestial mechanics, fluid dynamics, and plasma physics
Geometry, Topology, and Mathematical Structures in Physics
- Differential geometry, symplectic geometry, and Riemannian manifolds
- Topological invariants and their physical applications
- Geometric quantization and category-theoretic approaches
- Mathematical frameworks for modern theoretical physics
Computational and Numerical Methods in Mathematical Physics
- Simulation of physical systems using numerical algorithms
- Discretization methods, spectral techniques, and finite-element analysis
- Symbolic computation and high-performance computing
- Data-driven modeling and machine learning for physical systems