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physics background

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Enhanced Promptcomplexity of subatomic particles, relativistic energies, quantum fluctuations, entangled particles, wave-particle duality, uncertainty principle, Heisenberg's uncertainty principle, Schrödinger's equation, particle accelerator experiments, cosmological expansion, gravitational waves, dark matter, dark energy, Higgs boson discovery, Feynman diagrams, perturbation theory, scattering cross-sections, decay rates, Planck constant, Dirac equation, Klein-Gordon equation, Lagrangian mechanics, Hamiltonian dynamics, Noether's theorem, conservation laws, symmetries, isospin, spin-statistics theorem, strong nuclear force, weak nuclear force, electromagnetic force, gravitational force, Yang-Mills theory, gauge theories, Kaluza-Klein compactification, braneworld scenarios, cosmic strings, topological defects, domain walls, inflationary models, multiverse hypothesis, eternal inflation, cyclic models, string theory, loop quantum gravity, Causal Dynamical Triangulation, asymptotic safety scenario, holographic principle, AdS/CFT correspondence, entropic forces, anthropic reasoning, fine-tuning problem, cosmological constant problem, neutrino masses, CP violation, CKM matrix, Standard Model of particle physics, beyond the Standard Model, supersymmetry, extra dimensions, gravitons, graviphotons, axions, sterile neutrinos, moduli fields, scalar fields, pseudoscalar fields, vector fields, tensor fields, spinors, fermions, bosons, Majorana mass terms, Weinberg angle, Cabibbo angle, Kobayashi-Maskawa mixing angles, electroweak symmetry breaking, QCD confinement, hadronization, fragmentation functions, parton distributions, deep inelastic scattering, jet production, heavy ion collisions, quark-gluon plasma, thermalization, freeze-out, chiral symmetry restoration, deconfinement phase transition, lattice gauge theory, Monte Carlo simulations, computational complexity theory, renormalization group flow, fixed points, critical exponents, scaling laws, universality classes, topological phases, anyon statistics, non-Abelian anyons, Chern-Simons term, topological insulators, superconductors, superfluids, Bose-Einstein condensates, Fermi liquids, Landau's Fermi liquid theory, electron-electron interactions, phonons, magnons, plasmons, excitons, Cooper pairs, BCS theory, superconductivity, superfluidity, superfluid helium, vortex lattices, vortex rings, solitons, kinks, skyrmions, instantons, monopoles, dyons, magnetic monopoles, dyonic strings, Calabi-Yau manifolds, Calabi-Yau metrics, Ricci-flat metrics, Einstein manifolds, Kähler-Einstein metrics, Calabi-Yau fibrations, mirror symmetry, T-duality, S-duality, U-duality, M-theory, F-theory, heterotic string theory, type I string theory, type II string theory, M-theory compactifications, warped geometry, Calabi-Yau spaces, Gopakumar-Vafa duality, geometric engineering, flux compactifications, orientifold orbifolds, blow-up modes, D-brane instantons, brane world-volume, open string theory, closed string theory, tachyon condensation, D-branes, NS5-branes, D0-branes, D6-branes, D8-branes, D10-branes, NS5-brane charge, D-instantons, Euclidean signature, Lorentzian signature, Wick rotation, dimensional regularization, Pauli-Villars regularization, Bogolyubov-Parasyuk-Hepp-Zimmermann (BPHZ) method, pinch technique, asymptotic freedom, running coupling constants, anomalous dimensions, beta functions, gamma functions, zeta function, Riemann zeta function, Euler-Maclaurin summation formula, Hurwitz zeta function, Clausen's identity, Riemann-Roch theorem, Atiyah-Singer index theorem, Gauss-Bonnet theorem, Palatini identity, Bianchi identities, Jacobi identity, Poisson bracket, commutator, anticommutator, covariant derivative, Christoffel symbols, Levi-Civita connection, Riemann curvature tensor, Ricci tensor, Ricci scalar, Weyl tensor, Kretschmann scalar, Cotton tensor, Bach