Theoretical Physics & Mathematical Models

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Abstractions about mathematical representations used across particle, field, wave, and statistical physics. They include invariants and operators, interaction diagrams, scattering and transport, polarization, symmetry, approximation methods, and idealized particles or forces.

34 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Adiabatic invariant — A quantity that remains approximately constant while a system's parameters vary sufficiently slowly relative to its intrinsic dynamics.
• Antisymmetrizer — A linear projection that averages all particle-label permutations with their signs, extracting the totally antisymmetric component required for identical fermions.
• Autowave — A self-sustaining nonlinear wave that propagates through an active medium supplied with distributed energy.
• Bootstrap model — A historical strong-interaction hypothesis that hadrons are self-consistently composed of and bound by exchanges of other hadrons, with no privileged elementary member.
• Born reciprocity — The proposed symmetry exchanging spacetime coordinates with energy–momentum coordinates, up to signs and scale factors.
• Cabibbo–Kobayashi–Maskawa matrix — A unitary matrix relating quark flavor eigenstates to weak-interaction eigenstates in the Standard Model.
• Chaotic scattering — Scattering dynamics in which arbitrarily small changes in incoming conditions produce fractal changes in exit channel, angle or delay time.
• Coulomb's law — Relate the electrostatic force between ideal point charges to the product of their charges and the inverse square of their separation, directed along the line joining them and modified by the medium.
• Critical dimension — A spatial dimension at which the existence or universality behavior of a phase transition changes, including lower and upper critical dimensions.
• Crystal Ball function — A probability-density shape joining a Gaussian core continuously and differentiably to a one-sided power-law tail.
• DeWitt notation — A condensed field-theory notation that folds discrete field labels and continuous spacetime coordinates into generalized indices, with repeated indices implying both sums and integrals.
• Diagrammatic Monte Carlo — A stochastic numerical method sampling and summing selected Feynman-diagram expansions for interacting many-body systems.
• Double electron capture — A rare nuclear-decay mode in which two bound electrons are captured by two protons, converting them into neutrons while atomic number falls by two and mass number is unchanged.
• Eightfold way (physics) — An SU(3)-flavor symmetry classification organizing hadrons into multiplets by isospin and hypercharge.
• Einstein–Brillouin–Keller method — A semiclassical quantization method assigning action-integral conditions, including Maslov phase corrections, to invariant tori of integrable classical systems.
• Ewald summation — A convergent decomposition of periodic long-range interaction sums into rapidly decaying real-space and reciprocal-space contributions.
• Faraday paradox — A class of electromagnetic-induction setups whose observed electromotive force appears inconsistent with a naive magnetic-flux-change calculation.
• Fifth force — A hypothesized fundamental interaction beyond gravitation, electromagnetism and the strong and weak nuclear interactions.
• Fourier number — A dimensionless elapsed time for diffusion, equal to diffusivity times time divided by the square of a characteristic length.
• Frenkel–Kontorova model — A model of elastically coupled particles in a periodic substrate potential that captures competition between a preferred spacing and an imposed lattice.
• Harmonic measure — A boundary probability measure giving the likelihood that Brownian motion started inside a domain first exits through each boundary subset, equivalently representing solutions of the Dirichlet problem.
• Jost function — A scattering-theory Wronskian whose zeros and analytic structure encode bound states, resonances, and phase shifts of a radial wave equation.
• Manley–Rowe relations — Conservation relations that constrain energy or action exchange among frequency components participating in a lossless nonlinear wave interaction.
• Method of image charges — An electrostatic solution method that replaces conductor boundaries with fictitious charges chosen to reproduce the required boundary conditions.
• Mirror symmetry (string theory) — A duality pairing Calabi–Yau geometries whose associated string compactifications are physically equivalent while exchanging complex and symplectic geometric data.
• Neumann–Poincaré operator — A boundary integral operator built from the normal derivative of the Laplace fundamental solution and used to reduce harmonic boundary-value problems to Fredholm integral equations.
• Okorokov effect — Resonant coherent excitation of fast ions channeled through a crystal when their internal transition frequency matches the periodic lattice-field frequency in the ion frame.
• Point particle — An idealized physical object with finite properties such as mass or charge but zero spatial extent at the modeling scale.
• Polarization (waves) — The geometric pattern traced by a transverse wave’s oscillating field or displacement in the plane perpendicular to propagation.
• Relativistic electromagnetism — The unified spacetime formulation in which electric and magnetic fields are observer-dependent components of one electromagnetic field tensor.
• Rishon model — A speculative preon model representing quarks and leptons as three-preon combinations of two fundamental rishon types with assigned charge and color structure.
• Test particle — An idealized probe whose selected property responds to a field while its own influence on the modeled system is treated as negligible.
• Transmission coefficient — A convention-dependent amplitude, intensity, probability, or power ratio quantifying how much of an incident wave or flux passes through a boundary or barrier.
• Transport integrals — A family of special integrals weighting powers of a dimensionless variable by a thermal occupation-response kernel in solid-state transport theory.