um ## Tags - Topics: [[landing/docs/Contents/Exobrain/Topics/Science|Science]] [[Mathematics|Mathematics]] - Additional: ## Significance - Allowing to predict, control, design and explain any physical system, which is all systems in reality. ## Definitions - [[Mathematics]] constrained by physical reality. ## Technical summaries - Equations describing physical systems. ## Main resources - [Physics - Wikipedia](https://en.wikipedia.org/wiki/Physics) <iframe src="https://en.wikipedia.org/wiki/Physics" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - Stanford [Leonard Susskind The Theoretical Minimum Course](https://theoreticalminimum.com/courses) and other university lectures linked in the various pages of subfields - Hardest way to learn physics: [geometry of physics in nLab](https://ncatlab.org/nlab/show/geometry+of+physics) - [Classical Mechanics: John R. Taylor: 9781891389221: Amazon.com: Books](https://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X) - [best physics books - Hledat Googlem](https://www.google.com/search?q=best+physics+books&sca_esv=e14f95cbc2b145ff&sca_upv=1&sxsrf=ADLYWIKtFzCIMux6n-YEJCoeYSSUEq5ASA%3A1727604729394&ei=-Sf5ZvzZF8Dn7_UPxuSD2QI&ved=0ahUKEwi8utSR9eeIAxXA87sIHUbyICsQ4dUDCA8&uact=5&oq=best+physics+books&gs_lp=Egxnd3Mtd2l6LXNlcnAiEmJlc3QgcGh5c2ljcyBib29rczIFEAAYgAQyBRAAGIAEMgsQABiABBiRAhiKBTIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgARI_UdQuzlY50ZwAngBkAEAmAF-oAHPC6oBAzkuNrgBA8gBAPgBAZgCEaAClg3CAgoQABiwAxjWBBhHwgINEAAYgAQYsAMYQxiKBcICDhAAGLADGOQCGNYE2AEBwgITEC4YgAQYsAMYQxjIAxiKBdgBAcICChAjGIAEGCcYigXCAgsQLhiABBjRAxjHAcICChAAGIAEGBQYhwKYAwCIBgGQBhO6BgYIARABGAmSBwQ2LjExoAewXg&sclient=gws-wiz-serp) - [Search | MIT OpenCourseWare | Free Online Course Materials](https://ocw.mit.edu/search/) ## Landscapes - [Outline of physics - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_physics) <iframe src="https://en.wikipedia.org/wiki/Outline_of_physics" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - [The Map of Physics - YouTube](https://www.youtube.com/watch?v=ZihywtixUYo) <iframe title="The Map of Physics" src="https://www.youtube.com/embed/ZihywtixUYo?feature=oembed" height="113" width="200" allowfullscreen="" allow="fullscreen" style="aspect-ratio: 1.76991 / 1; width: 100%; height: 100%;"></iframe> - [[Mathematical physics]] - By domain - [[Classical mechanics]] - [[Fluid mechanics]] - [[Field theory]] - [[Electromagnetism]] - [[Optics]] - [[Theory of relativity]] - [[Special relativity]] - [[General relativity]] - [[Quantum mechanics]] - [[Statistical mechanics]] - [[Thermodynamics]] - [[Non-equilibrium statistical mechanics]] - [[Non-equilibrium thermodynamics]] - [[Dynamical systems theory]] - [[Information theory]] - Unity - [[Relativistic quantum mechanics]] - [[Quantum field theory]] - [[Standard Model of Particle Physics]] - [[Quantum electrodynamics]] - [[Quantum chromodynamics]] - [[Quantum statistical mechanics]] - [[Quantum field statistical mechanics]] - [[Quantum information theory]] - [[Loop Quantum Gravity]] - [[String theory]] - [[M Theory]] - [[Causal sets]] - [[Cosmology]] - [[Interdisciplinarity]] - [[Biophysics]] - [[Neurophysics]] - [[Technology]] - [[Computing]] - [[Quantum computing]] - [[Thermodynamic computing]] - [[Artificial Intelligence]] - [[Quantum machine learning]] - [[Thermodynamic AI]] - [[Power generation]] - [[Black hole]] - [[Interpretations of quantum mechanics]] - [[Artificial Intelligence x Physics]] #### Fundamental equations of the universe [X](https://x.com/skdh/status/1847616858398089303) [[Images/71ede449f0921c12dfd2b4686b47b940_MD5.jpeg|Open: Pasted image 20241022020353.png]] ![[Images/71ede449f0921c12dfd2b4686b47b940_MD5.jpeg]] [[Images/16c21171fb1dff8faafcc146b896f06e_MD5.jpeg|Open: Pasted image 20241006100449.png]] ![[Images/16c21171fb1dff8faafcc146b896f06e_MD5.jpeg]] - [[Standard Model of Particle Physics#Lagrangian]] ![[Standard Model of Particle Physics#Lagrangian]] ## Deep dives - [[Natural science#Structure of reality from first principles]] ![[Natural science#Structure of reality from first principles]] - [List of unsolved problems in physics - Wikipedia](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics) - <iframe src="https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - [Every Thing in Space - YouTube](https://www.youtube.com/watch?v=uniGQrGLEoI) - [The Map of Black Holes | Black Holes Explained - YouTube](https://www.youtube.com/watch?v=Wf0uxjWGwPk) - [physics in nLab](https://ncatlab.org/nlab/show/physics) ## Resources Stanford: classical mechanics, quantum mechanics, statistical mechanics, cosmology, particle physics, string theory https://theoreticalminimum.com/ MIT: classical mechanics https://www.youtube.com/playlist?list=PLyQSN7X0ro203puVhQsmCj9qhlFQ-As8e https://www.youtube.com/playlist?list=PLUl4u3cNGP61qDex7XslwNJ-xxxEFzMNV electricity and magnetism electromagnetism https://www.youtube.com/playlist?list=PLyQSN7X0ro2314mKyUiOILaOC2hk6Pc3j https://www.youtube.com/playlist?list=PLmNMkuCOhP2sGhvByEAq2LAS2QMFDPQM- quantum physics https://www.youtube.com/playlist?list=PLUl4u3cNGP61-9PEhRognw5vryrSEVLPr https://www.youtube.com/playlist?list=PLUl4u3cNGP60cspQn3N9dYRPiyVWDd80G https://www.youtube.com/playlist?list=PLUl4u3cNGP60QlYNsy52fctVBOlk-4lYx https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L vibration and waves https://www.youtube.com/playlist?list=PLUl4u3cNGP61R5sPDPKVfcFlu95wSs2Kx https://www.youtube.com/playlist?list=PLyQSN7X0ro22WeXM2QCKJm2NP_xHpGV89 https://www.youtube.com/playlist?list=PLUl4u3cNGP62JTiv0epD_FMmUV6Y7wMv_ history of 20th century https://www.youtube.com/playlist?list=PLUl4u3cNGP63bAfjGas3TuA4ZCPUtN6Xf general relativity https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx special relativity https://www.youtube.com/playlist?list=PLUl4u3cNGP61Zc3rR6wVM0kpsiyIq0fk8 nuclear and particle physics https://www.youtube.com/playlist?list=PLUl4u3cNGP60Do91PdN978llIsvjKW0au relativistic quantum field theory https://www.youtube.com/playlist?list=PLUl4u3cNGP61AV6bhf4mB3tCyWQrI_uU5 statistical mechanics https://www.youtube.com/playlist?list=PLUl4u3cNGP60gl3fdUTKRrt5t_GPx2sRg https://www.youtube.com/playlist?list=PLUl4u3cNGP63HkEHvYaNJiO0UCUmY0Ts7 atomic nucelar and optical physics https://www.youtube.com/playlist?list=PLUl4u3cNGP62FPGcyFJkzhqq9c5cHCK32 https://www.youtube.com/playlist?list=PLUl4u3cNGP62uOSArqLf4vNLiZtgIRm1K nuclear engineering https://www.youtube.com/playlist?list=PLUl4u3cNGP61FVzAxBP09w2FMQgknTOqu solid state physics https://www.youtube.com/playlist?list=PLcxQMvk7OdDN2B2M9tLwr9bnsjEIIxZLl experimental physics https://www.youtube.com/playlist?list=PLUl4u3cNGP6393Jj6WMmNd1_pOs0UDq2R physics experiments https://www.youtube.com/playlist?list=PL7145A9AA4BAF35FC thermodynamics of materials https://www.youtube.com/playlist?list=PLUl4u3cNGP61g-yRbJz4ghFPJLiok1HxX thermodynamics and kinetics https://www.youtube.com/playlist?list=PLA62087102CC93765 early universe https://www.youtube.com/playlist?list=PLUl4u3cNGP61Bf9I0WDDriuDqEnywoxra physical chemistry https://www.youtube.com/playlist?list=PLUl4u3cNGP62RsEHXe48Imi9-87FzQaJg optics https://www.youtube.com/playlist?list=PLEA084AC2DD3CEC09 thermodynamics https://www.youtube.com/playlist?list=PLF6C6594F42ECEE0D cosmology https://www.youtube.com/playlist?list=PL4BUyFYOFtUZIUtcSDo6vm4HPxS9aZmHC engineering dynamics https://www.youtube.com/playlist?list=PLUl4u3cNGP62esZEwffjMAsEMW_YArxYC string theory and holographic duality https://www.youtube.com/playlist?list=PLUl4u3cNGP633VWvZh23bP6dG80gW34SU plasma diagnostics https://www.youtube.com/playlist?list=PLUl4u3cNGP61wK-NwYKZMuABl_eHBmhu4 nuclear physics https://www.youtube.com/playlist?list=PLOarn8QL6W_LOBTvWwLac5VCxJpkiHa-e black holes https://www.youtube.com/playlist?list=PL5CA9864EFB258E8A yale electromagnetism https://www.youtube.com/playlist?list=PLB1A0BF14EB31C3BE Physics Sean Carroll [The Biggest Ideas in the Universe! - YouTube](https://www.youtube.com/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX) [An Elegant Structural Overview of Modern Theoretical Physics - YouTube](https://www.youtube.com/watch?v=2bi5G6plWCI) An Elegant Structural Overview of Modern Theoretical Physics Nonequilibrium thermodynamics, nonequilibrium statistical mechanics [Non-equilibrium statistical physics - YouTube](https://www.youtube.com/playlist?list=PL04QVxpjcnjjoN7xfc7Vy63uUSkDlOYiU) [Fluctuations in Nonequilibrium Systems: Theory and Applications - YouTube](https://www.youtube.com/playlist?list=PL04QVxpjcnjgmUoD6tlO_0YT1k5GYgQWi) [Nonequilibrium Stat Mechanics - YouTube](https://www.youtube.com/playlist?list=PLCVqYvWXt6ZM3Sh5qbN2SAWABpinU6smE) [nonequilibrium - YouTube](https://www.youtube.com/playlist?list=PLrbFeBstDbRLw9kwTqJJsD490YcPEU8x8) [Nonequilibrium - YouTube](https://www.youtube.com/playlist?list=PLsdMv0E_Hm4bavLh1nm12XvjHwlekZ-WZ) [Statistical Mechanics 1 (Equilibrium & Non-equilibrium) - YouTube](https://www.youtube.com/playlist?list=PLv64M6nvmocsPYna-WHr0mX8dSp_OEgVV) [Non Equilibrium Stat Mech - YouTube](https://www.youtube.com/playlist?list=PLXi9EP7hqH1aFw8_-kf-h70zSIXUARLNH) [School on Emergent Phenomena in Non-Equilibrium Quantum Many-Body Systems - YouTube](https://www.youtube.com/playlist?list=PLg0_ydgtbHGGQM_VDY9562kPfFHCn_C_z) [Non-Equilibrium Thermodynamics (NET) - YouTube](https://www.youtube.com/playlist?list=PLMi1tmgJbrSINVKIVjLLqkARXsixSftqf) [Physics - Nonequilibrium Statistical Mechanics - YouTube](https://www.youtube.com/playlist?list=PLbMVogVj5nJQqNx0ElSk3Ip04Ofg7B22W) [How_to_learn_Physics_from_the_ground_up/README.md at main · joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up · GitHub](https://github.com/joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up/blob/main/README.md) [GitHub - llSourcell/Learn_Physics_in_2_Months: This is the curriculum for "Learn Physics in 2 Months" by Siraj Raval on Youtube](https://github.com/llSourcell/Learn_Physics_in_2_Months) [GitHub - comp-physics/awesome-numerics: Resources for learning about numerical methods.](https://github.com/comp-physics/awesome-numerics) [GitHub - Hridoy-31/physics-video-courses: List of Physics courses with video lectures.](https://github.com/Hridoy-31/physics-video-courses) [How_to_learn_Physics_from_the_ground_up/README.md at main · joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up · GitHub](https://github.com/joaocarvalhoopen/How_to_learn_Physics_from_the_ground_up/blob/main/README.md) [GitHub - llSourcell/Learn_Physics_in_2_Months: This is the curriculum for "Learn Physics in 2 Months" by Siraj Raval on Youtube](https://github.com/llSourcell/Learn_Physics_in_2_Months) [GitHub - comp-physics/awesome-numerics: Resources for learning about numerical methods.](https://github.com/comp-physics/awesome-numerics) https://brilliant.org/courses/ [[nonAI mathcode long important]] ## Brainstorming We will crack the source of of our simulation The source code of our simulation, the standard model of particle physics! Almost cracked? Quantum gravity and some other problems are missing! What is measurement on the fundamental level? The capability of AI systems I'm the most interested in is if you gave the system all of classical mechanics, if it could derive general relativity and quantum mechanics from it, which seems to be a stronger out of distribution generalization than the current types of systems can do, but I'm open to be mistaken. And give it all (most of) known empirical data from experiments before the phase shift and derive it from these too. Universe is one gigantic system of quantum harmonic oscillators composing into complex higher order harmonic oscillators god is the quantum harmonic oscillator The mathematician in me is crying when it's observing the physicist trying to learn physics and doing all the mathematically illegal operations and approximations that are legal in physics Physics lectures are like candies Is space an objective container or relational between objects? What if there is no theory of quantum gravity and we need complete paradigm shift out of our current maps? We might have to transcend the mathematical concept of dimensions altogether in fundamental physics! Solving quantum gravity might reveal a glitch in the fabric of spacetime and fundamental particles and forces or strings or whatever is under all, that allows for arbitrary code execution exploit to edit or spawn arbitrary structure and laws! How does the equation predicting all of our current measured and future empirical data looks like? The whole world is one big collection of interconnected changes, and derivatives describe their pace. ## Additional topics - [The Map of Superconductivity - YouTube](https://www.youtube.com/watch?v=bD2M7P6dTVA) - [Atomic Spectroscopy Explained in 9 Slides - YouTube](https://www.youtube.com/watch?v=crWBFuUW6kI) - [The Incredible Science of CERN - YouTube](https://www.youtube.com/watch?v=hAK6ovQQqtc) ## AI landscapes #### 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