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Mathematical Physics

Mathematical Physics involves the application of mathematics to problems in physics and the development of mathematical methods suitable for the formulation of physical theories. It bridges the gap between mathematics and physics and contributes to the theoretical foundations of both disciplines.
Sub-categories:

Explore the mathematical framework of quantum theory, focusing on wave functions, quantum states, and the probabilistic nature of quantum phenomena.

Dive into the geometric theory of gravitation and spacetime, analyzing Einstein's field equations and their implications in cosmology.

Study the mathematical formulation of systems with a large number of degrees of freedom and the derivation of macroscopic properties from microscopic laws.

Understand the principles of classical and quantum fields, with applications ranging from electromagnetism to quantum chromodynamics.

Revisit Newton's laws of motion through advanced mathematical tools such as Lagrangian and Hamiltonian formulations.

Explore complex systems where nonlinearities play a crucial role, including chaos theory and solitons.

Delve into the theory combining quantum mechanics and special relativity, which is essential for understanding particle physics.

Investigate the theoretical framework where point-like particles are replaced by one-dimensional strings, aiming to unify gravity with other fundamental forces.

Apply numerical methods and algorithms to solve complex physical problems that are intractable by analytical means.

Uncover attempts to formulate a quantum theory of gravity, addressing the reconciliation of general relativity with the principles of quantum mechanics.

Learn about the theoretical model proposing a relation between two basic classes of elementary particles – bosons and fermions.

Focus on the study of the macroscopic and microscopic physical properties of matter in solid and liquid states using mathematical models.

Examine the branch of physical science that describes heat, work, temperature, and energy transfer in physical, chemical, and biological systems.

Investigate quantum field theories that are invariant under homeomorphisms, highlighting the role of topology in physical phenomena.

Study systems with many components that have rich interactions and behaviors, such as networks, biological systems, and social systems.

Explore the theory surrounding the storage, processing, and transmission of information using quantum mechanical systems.