History of quantum field theory
The third thread in the development of quantum field theory was the need to handle the statistics of many-particle systems consistently and with ease. In 1927, Pascual Jordan tried to extend the canonical quantization of fields to the many-body wave functions of identical particles using a formalism which is known as statistical transformation theory; this procedure is now sometimes called second quantization. In 1928, Jordan and Eugene Wigner found that the quantum field describing electrons, or other fermions, had to be expanded using anti-commuting creation and annihilation operators due to the Pauli exclusion principle (see Jordan–Wigner transformation). This thread of development was incorporated into many-body theory and strongly influenced condensed matter physics and nuclear physics.
Quantum configuration space
In quantum field theory, the quantum configuration space, the domain of the wave functions formula_12, is larger than the classical configuration space. While in the classical theory we can restrict ourselves to suitably smooth fields, in quantum field theory we are forced to allow distributional field configurations. In fact, in quantum field theory physically interesting measures are concentrated on distributional configurations.