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Physics

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Significance

  • Allowing to predict, control, design and explain any physical system, which is all systems in reality.

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  • Equations describing physical systems.

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Branches

  • Physics is a vast field with numerous branches and sub-disciplines, each exploring different aspects of matter, energy, and the fundamental forces of nature. Here's a comprehensive list of the various branches of physics:

1. Classical Physics

  • Mechanics
    • Classical Mechanics
    • Continuum Mechanics
    • Fluid Mechanics
    • Statics
    • Dynamics
    • Kinematics
    • Acoustics
  • Thermodynamics
  • Electromagnetism
    • Electrostatics
    • Electrodynamics
    • Magnetostatics
    • Optics
    • Geophysics

2. Modern Physics

  • Quantum Physics
    • Quantum Mechanics
    • Quantum Field Theory
    • Quantum Electrodynamics
    • Quantum Chromodynamics
    • Quantum Optics
    • Quantum Thermodynamics
  • Relativity
    • Special Relativity
    • General Relativity
  • Particle Physics
    • Nuclear Physics
    • High Energy Physics
    • Particle Astrophysics
  • Condensed Matter Physics
    • Solid State Physics
    • Superconductivity
    • Semiconductor Physics
    • Nanophysics
  • Plasma Physics
  • Atomic, Molecular, and Optical Physics
  • Computational Physics

3. Applied Physics

  • Medical Physics
  • Biophysics
  • Chemical Physics
  • Geophysics
  • Meteorology
  • Oceanography
  • Environmental Physics
  • Engineering Physics
  • Acoustics
  • Photonics
  • Nanotechnology
  • Materials Science

4. Astrophysics and Cosmology

  • Astrophysics
    • Stellar Astrophysics
    • Galactic Astrophysics
    • Extragalactic Astrophysics
    • Planetary Science
    • Space Physics
  • Cosmology
    • Physical Cosmology
    • Observational Cosmology
    • Cosmogony

5. Theoretical Physics

  • Mathematical Physics
  • Classical Field Theory
  • Theoretical Mechanics
  • Statistical Mechanics
  • Theoretical Particle Physics
  • Theoretical Astrophysics
  • String Theory

6. Experimental Physics

  • Particle Detectors
  • Experimental Techniques and Instrumentation
  • Data Analysis Techniques

7. Interdisciplinary Fields

  • Physical Chemistry
  • Atmospheric Physics
  • Earthquake Physics
  • Psychophysics
  • Econophysics
  • Agrophysics
  • Neurophysics
  • Biochemical Physics
  • Crystallography

8. Emerging Fields

  • Quantum Computing
  • Quantum Cryptography
  • Quantum Information Theory
  • Quantum Gravity
  • Dark Matter and Dark Energy Studies
  • Gravitational Wave Astronomy

Map of mathematics of physics

Here's the text with added around the topics according to your instructions:

Classical Mechanics: - [[Calculus]]: derivatives, integrals, differential equations (ordinary and partial), variational calculus - [[Linear algebra]]: vectors, matrices, eigenvalues, eigenvectors - [[Variational principles]]: Euler-Lagrange equations, Hamilton's principle - [[Lagrangian and Hamiltonian mechanics]]: generalized coordinates, phase space, Poisson brackets - [[Dynamical systems]]: stability analysis, bifurcations, chaos theory - [[Perturbation theory]]: regular and singular perturbations - [[Numerical methods]]: Runge-Kutta, finite difference, finite element

[[Electromagnetism]]: - [[Vector calculus]]: gradient, divergence, curl, Stokes' theorem, Green's theorem - [[Partial differential equations]]: Maxwell's equations, wave equation, Helmholtz equation - Complex analysis: analytic functions, Cauchy-Riemann equations, residue theorem - [[Tensor analysis]]: electromagnetic field tensor, stress-energy tensor - [[Differential forms]]: exterior derivative, Hodge star operator - [[Gauge theory]]: gauge transformations, fiber bundles, connections - [[Numerical methods]]: finite difference time domain (FDTD), method of moments (MoM)

[[Thermodynamics and Statistical Mechanics]]: - Probability theory: random variables, probability distributions, central limit theorem - [[Differential equations]]: transport equations, Fokker-Planck equation - [[Multivariate calculus]]: Jacobians, Hessians, Lagrange multipliers - [[Linear algebra]]: matrix exponentials, eigenvalue problems - Information theory: entropy, mutual information, Kullback-Leibler divergence - [[Stochastic processes]]: Markov chains, Brownian motion, Langevin equation - [[Monte Carlo methods]]: Metropolis-Hastings algorithm, Gibbs sampling

Quantum Mechanics: - [[Linear algebra]]: Hilbert spaces, linear operators, eigenvalues, eigenvectors - [[Differential equations]]: Schrödinger equation, Dirac equation, Klein-Gordon equation - Probability theory: Born rule, density matrices, quantum measurement - [[Group theory]]: symmetries, representations, Lie groups, Lie algebras - [[Functional analysis]]: self-adjoint operators, spectral theory, Banach spaces - [[Perturbation theory]]: time-independent and time-dependent perturbation theory - [[Numerical methods]]: finite difference, variational methods, quantum Monte Carlo

Quantum Field Theory: - [[Tensor analysis]]: Lorentz transformations, spinors, Clifford algebras - [[Group theory]]: Lie groups (U(1), SU(2), SU(3)), Lie algebras, representation theory - [[Differential geometry]]: fiber bundles, connections, curvature, characteristic classes - [[Topology]]: homotopy groups, homology, cohomology, index theorems - Complex analysis: dispersion relations, Feynman integrals, renormalization - [[Functional analysis]]: path integrals, operator algebras, BRST quantization - [[Perturbation theory]]: Feynman diagrams, renormalization group, effective field theories - [[Lattice field theory]]: lattice gauge theory, lattice QCD

[[General Relativity]]: - [[Differential geometry]]: manifolds, tangent spaces, differential forms, Riemannian geometry - [[Tensor analysis]]: Riemann curvature tensor, Ricci tensor, energy-momentum tensor - [[Partial differential equations]]: Einstein field equations, wave equations in curved spacetime - [[Variational principles]]: Einstein-Hilbert action, Palatini formalism - [[Topology]]: causal structure, singularity theorems, black hole thermodynamics - [[Numerical relativity]]: ADM formalism, BSSN formalism, pseudospectral methods

[[Particle Physics]]: - [[Group theory]]: representation theory, Lie groups (U(1), SU(2), SU(3)), grand unification - [[Differential geometry]]: gauge theories, spontaneous symmetry breaking, Higgs mechanism - [[Topology]]: instantons, monopoles, solitons, anomalies - Complex analysis: dispersion relations, analytic S-matrix theory - [[Functional analysis]]: path integrals, operator product expansion, conformal field theory - [[Perturbative QCD]]: Feynman diagrams, parton model, factorization theorems - [[Lattice QCD]]: discretization of QCD, numerical simulations

[[Condensed Matter Physics]]: - [[Differential equations]]: Schrödinger equation, Ginzburg-Landau theory, Bogoliub

ov-de Gennes equations - [[Linear algebra]]: tight-binding models, Wannier functions, Bloch functions - Probability theory: stochastic processes, master equations, fluctuation-dissipation theorem - [[Topology]]: topological insulators, Berry phase, Chern numbers - [[Group theory]]: space groups, point groups, representation theory - [[Many-body theory]]: Green's functions, Feynman diagrams, renormalization group - [[Numerical methods]]: density functional theory (DFT), quantum Monte Carlo, tensor networks

[[Fluid Dynamics]]: - [[Partial differential equations]]: Navier-Stokes equations, Euler equations, Boltzmann equation - [[Vector calculus]]: vorticity, circulation, Kelvin's theorem, Helmholtz decomposition - Complex analysis: conformal mapping, potential flow, Joukowsky transform - [[Perturbation theory]]: boundary layer theory, Kolmogorov's theory of turbulence - [[Numerical methods]]: finite volume methods, spectral methods, lattice Boltzmann methods

[[Plasma Physics]]: - [[Partial differential equations]]: magnetohydrodynamic (MHD) equations, Vlasov equation - [[Kinetic theory]]: Boltzmann equation, Fokker-Planck equation, quasilinear theory - Statistical mechanics: BBGKY hierarchy, kinetic equations - [[Fluid dynamics]]: ideal MHD, resistive MHD, two-fluid models - [[Numerical methods]]: particle-in-cell (PIC) methods, gyrokinetic simulations

[[Astrophysics and Cosmology]]: - [[General relativity]]: Friedmann equations, cosmic microwave background, gravitational lensing - [[Fluid dynamics]]: stellar structure, accretion disks, shock waves - [[Nuclear physics]]: nucleosynthesis, stellar evolution, supernovae - [[Particle physics]]: dark matter, neutrino astrophysics, cosmic rays - Statistical mechanics: galaxy clustering, large-scale structure, cosmological perturbation theory - [[Numerical methods]]: N-body simulations, smoothed particle hydrodynamics (SPH), adaptive mesh refinement (AMR)

[[Mathematical Physics (general tools)]]: - [[Differential equations]]: Sturm-Liouville theory, Green's functions, solitons - [[Functional analysis]]: Hilbert spaces, Banach spaces, distributions, Sobolev spaces - [[Operator theory]]: unbounded operators, spectral theory, C*-algebras - Probability theory: stochastic processes, stochastic differential equations, large deviations - [[Topology]]: algebraic topology, differential topology, Morse theory - [[Differential geometry]]: symplectic geometry, Poisson geometry, Kähler manifolds - [[Lie groups and algebras]]: representation theory, structure theory, Haar measure - [[Variational principles]]: calculus of variations, optimal control theory, conservation laws - [[Integrable systems]]: inverse scattering transform, Lax pairs, Painlevé transcendents - [[Nonlinear dynamics]]: bifurcation theory, pattern formation, synchronization - [[Numerical analysis]]: finite element methods, spectral methods, wavelets

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