Quantum field theory

Quantum field theory combines quantum mechanics with special relativity by describing particles as quantized excitations of fields that extend through space and time.

Quantum field: A field whose possible states are described by quantum mechanics and whose excitations can behave as particles. Quantum field theory assigns fields the fundamental role and treats particles as their excitations.
Quantum mechanics: A physical theory describing matter and radiation through states, probabilities, and quantized observables. Quantum field theory extends its quantum principles to fields and particle-changing processes.
Standard Model: The quantum field theory describing known elementary particles and three of their fundamental interactions. It is the most extensively tested application of quantum field theory.
Nonrelativistic quantum mechanics: Quantum mechanics formulated without the requirement of invariance under special relativity. Unlike quantum field theory, it usually assumes fixed particle number and nonrelativistic speeds.
Fock space: A Hilbert space that accommodates quantum states with varying numbers of particles. It lets quantum field theory describe particle creation and annihilation.
Special relativity: A theory of space and time in which physical laws are invariant across inertial frames and light has invariant speed. Quantum field theory is constructed to respect relativistic spacetime and causal structure.
Quantum electrodynamics: The quantum field theory of electromagnetic interactions between charged particles and photons. It provides a precise example of quantum fields making highly accurate predictions.
Classical field theory: A framework describing physical quantities distributed through space and time using classical, nonquantized fields. It has fields but not the quantum excitations and probabilities central to this framework.
Creation and annihilation operators: Operators that add or remove a quantum of a specified mode from a quantum state. They express how field interactions change particle number.
Lagrangian mechanics: A formulation of classical mechanics based on a function whose action is stationary along physical trajectories. Field theories often begin with a Lagrangian density that specifies their dynamics.

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