Second quantization is the formalism of quantum field theory in which fields, rather than individual particles, are the fundamental quantized entities: classical fields are promoted to field operators acting on a Fock space, with creation and annihilation operators that add or remove field excitations (particles), governed by commutation relations (for bosons, symmetric wavefunctions) or anti-commutation relations (for fermions, antisymmetric wavefunctions enforcing the Pauli exclusion principle). This extends first quantization—ordinary quantum mechanics, in which wavefunctions and operators describe fixed numbers of individual particles via the Schrödinger equation on a Hilbert space—to systems with variable particle number and particle creation/annihilation, situating the theory within quantum field theory as the union of quantum mechanics and relativistic field theory.
Second quantization is the formalism of quantum field theory in which fields, rather than individual particles, are the fundamental quantized entities: classical fields are promoted to field operator…