Field and string theory models and techniques

Mathematical frameworks and methods for formulating and analyzing quantum field theories and string theories, including perturbative, geometric, and duality-based approaches.

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Lagrangian mechanics: A formulation of classical mechanics in which motion follows from making the action stationary. The action principle underlying field-theory and string-theory formulations extends this framework.
Path integral formulation: A quantum formulation that expresses amplitudes as sums over possible histories weighted by their actions. It provides a common route to calculations in both field theory and string theory.
Standard Model: The quantum field theory describing known elementary particles and three of their fundamental interactions. It is the best-tested application of gauge quantum field theory.
Lattice field theory: A formulation of quantum field theory on discrete spacetime points and links. Its discretization contrasts with continuum formulations while enabling numerical study.
Quantum field theory: A framework combining quantum mechanics and special relativity in which fields are fundamental and particles are their excitations. It is the central framework whose models and techniques this page surveys.
Feynman diagrams: Diagrammatic representations of terms in perturbative expansions of quantum-field-theory amplitudes. They organize interaction calculations as expansions in coupling strengths.
Quantum chromodynamics: The gauge theory of quarks and gluons governing the strong interaction. Its confinement problem motivates lattice and other nonperturbative methods.
Supersymmetry: A symmetry relating bosons and fermions through transformations that exchange the two types of particles. Supersymmetric models often have cancellations and structures unavailable in generic theories.
Gauge theory: A field theory whose descriptions are invariant under local transformations of internal degrees of freedom. Gauge symmetry constrains interactions and determines much of the structure of particle theories.
Perturbation theory: A method for approximating solutions by expanding around a simpler, usually solvable, problem. Many practical predictions begin as expansions around a free or weakly coupled theory.