#### Map 1 # Comprehensive Map of Physics Physics is a vast field that seeks to understand the fundamental principles governing the universe. Below is an extensive map outlining the major branches and sub-disciplines of physics. --- ### A. Mechanics - **1. Newtonian Mechanics** - *a. Kinematics* - Motion in One Dimension - Motion in Two and Three Dimensions - *b. Dynamics* - Newton's Laws of Motion - Applications (Projectile Motion, Circular Motion) - *c. Work, Energy, and Power* - Work-Energy Theorem - Conservation of Energy - Power Calculations - *d. Momentum* - Linear Momentum and Impulse - Conservation of Momentum - Collisions (Elastic and Inelastic) - *e. Rotational Motion* - Angular Kinematics - Torque and Rotational Dynamics - Angular Momentum Conservation - *f. Gravitation* - Newton's Law of Universal Gravitation - Planetary Motion and Orbits - Gravitational Fields and Potential - **2. Fluid Mechanics** - *a. Fluid Statics* - Pressure and Density - Buoyant Forces and Archimedes' Principle - *b. Fluid Dynamics* - Continuity Equation - Bernoulli's Equation - Viscosity and Laminar Flow - Turbulence and Reynolds Number - **3. Oscillations and Waves** - *a. Simple Harmonic Motion* - Mass-Spring Systems - Pendulums - *b. Damped and Driven Oscillations* - *c. Wave Motion* - Wave Properties (Amplitude, Wavelength, Frequency) - Sound Waves and Acoustics - Standing Waves and Resonance ### B. Thermodynamics - **1. Temperature and Heat** - Thermal Expansion - Heat Transfer Methods (Conduction, Convection, Radiation) - **2. Laws of Thermodynamics** - Zeroth Law (Thermal Equilibrium) - First Law (Conservation of Energy) - Second Law (Entropy and Irreversibility) - Third Law (Absolute Zero) - **3. Thermodynamic Processes** - Isothermal, Adiabatic, Isobaric, Isochoric Processes - Heat Engines and Efficiency - **4. Statistical Mechanics** - Microstates and Macrostates - Boltzmann Distribution - Partition Functions ### C. Electromagnetism - **1. Electrostatics** - Electric Charge and Coulomb's Law - Electric Field and Electric Potential - Capacitance and Dielectrics - **2. Electric Circuits** - Current, Voltage, and Resistance - Ohm's Law and Kirchhoff's Laws - DC and AC Circuits - Circuit Components (Resistors, Capacitors, Inductors) - **3. Magnetism** - Magnetic Fields and Forces - Biot-Savart Law and Ampère's Law - Electromagnetic Induction (Faraday's Law) - **4. Maxwell's Equations** - Gauss's Laws for Electricity and Magnetism - Faraday's Law of Induction - Ampère's Law with Maxwell's Addition - **5. Electromagnetic Waves** - Wave Equation Solutions - Spectrum of Electromagnetic Radiation - Polarization and Modulation ### D. Optics - **1. Geometrical Optics** - Reflection and Refraction (Snell's Law) - Optical Instruments (Lenses, Mirrors, Prisms) - Ray Tracing Techniques - **2. Physical Optics** - Interference (Young's Double-Slit Experiment) - Diffraction (Single-Slit, Diffraction Gratings) - Polarization of Light - **3. Optical Phenomena** - Dispersion and Spectra - Holography - Fiber Optics --- ### A. Relativity - **1. Special Relativity** - Postulates of Relativity - Time Dilation and Length Contraction - Relativistic Energy and Momentum - Mass-Energy Equivalence (E=mc²) - **2. General Relativity** - Principle of Equivalence - Curvature of Spacetime - Gravitational Lensing - Black Holes and Event Horizons ### B. Quantum Mechanics - **1. Foundations** - Wave-Particle Duality - Heisenberg Uncertainty Principle - Schrödinger Equation (Time-Dependent and Time-Independent) - **2. Quantum States and Operators** - Quantum Superposition - Operators and Observables - Eigenvalues and Eigenfunctions - **3. Quantum Phenomena** - Quantum Tunneling - Quantum Entanglement and Nonlocality - Quantum Measurement Problem - **4. Interpretations of Quantum Mechanics** - Copenhagen Interpretation - Many-Worlds Interpretation - Pilot-Wave Theory ### C. Atomic and Molecular Physics - **1. Atomic Models** - Bohr Model - Quantum Atomic Models - **2. Electron Configurations** - Pauli Exclusion Principle - Hund's Rules - **3. Spectroscopy** - Emission and Absorption Spectra - Laser Physics ### D. Nuclear Physics - **1. Nuclear Structure** - Nuclear Forces and Binding Energy - Models of the Nucleus (Liquid Drop, Shell Model) - **2. Radioactivity** - Types of Decay (Alpha, Beta, Gamma) - Decay Chains and Half-Life - **3. Nuclear Reactions** - Fission and Fusion Processes - Nuclear Reactors and Weapons - **4. Applications** - Nuclear Medicine (PET, MRI) - Radiocarbon Dating ### E. Particle Physics - **1. Fundamental Particles** - Quarks and Leptons - Gauge Bosons (Photon, W/Z Bosons, Gluons) - Higgs Boson - **2. The Standard Model** - Electroweak Interaction - Quantum Chromodynamics - **3. Beyond the Standard Model** - Supersymmetry - Grand Unified Theories - [[String Theory]] - [[Loop Quantum Gravity]] - [[Causal sets]] ### F. Condensed Matter Physics - **1. Crystallography** - Crystal Lattices and Unit Cells - X-ray Diffraction - **2. Electronic Properties** - Band Theory of Solids - Conductors, Insulators, Semiconductors - **3. Quantum Hall Effect** - **4. Superconductivity** - Meissner Effect - BCS Theory --- ### A. Stellar Astrophysics - **1. Star Formation** - Nebular Hypothesis - Protostars and Main Sequence - **2. Stellar Evolution** - Red Giants and White Dwarfs - Supernovae and Neutron Stars - **3. Black Holes** - Formation and Types - Hawking Radiation ### B. Galactic Astronomy - **1. Structure of the Milky Way** - **2. Types of Galaxies** - Spiral, Elliptical, Irregular - **3. Galactic Dynamics** - Dark Matter Evidence ### C. Cosmology - **1. Big Bang Theory** - Cosmic Microwave Background - Nucleosynthesis - **2. Cosmic Inflation** - **3. Dark Energy and Accelerating Universe** - **4. Multiverse Theories** --- ### A. Biophysics - Molecular Motors - Neural Networks - Biomechanics ### B. Geophysics - Earth's Magnetic Field - Plate Tectonics - Seismology ### C. Chemical Physics - Reaction Dynamics - Spectroscopic Methods ### D. Environmental Physics - Climate Modeling - Atmospheric Physics --- ### A. Materials Science - Nanotechnology - Photonic Materials - Smart Materials ### B. Quantum Computing - Qubits and Quantum Gates - Quantum Algorithms ### C. Plasma Physics - Fusion Research - Space Plasmas ### D. Medical Physics - Imaging Techniques (X-rays, CT scans) - Radiation Therapy --- ### A. Conservation Laws - Energy - Linear and Angular Momentum - Charge ### B. Symmetry Principles - Noether's Theorem - CPT Symmetry ### C. Mathematical Methods - Differential Equations - Tensor Calculus - Group Theory ### D. Measurement and Units - SI Units - Dimensional Analysis - Error Analysis --- ### A. History of Physics - Classical Era (Aristotle to Newton) - Modern Era (Einstein to Present) ### B. Philosophy of Science - Scientific Method - Paradigm Shifts ### C. Ethics in Physics - Responsible Conduct of Research - Implications of Technological Advances --- ### A. Experimental Physics - Particle Accelerators - Telescopes and Detectors ### B. Computational Physics - Numerical Methods - Simulations and Modeling ### C. Data Analysis - Statistical Methods - Machine Learning in Physics --- This map provides a broad overview of physics, touching upon its many branches and the intricate topics within each. Physics is ever-evolving, with new discoveries and technologies continually expanding our understanding of the universe. #### Map 2 ### 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 - Heat Transfer - [[Statistical mechanics]] - Thermoelectricity - 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