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.
History of the philosophy of field theory
Fields become the fundamental object of study in quantum field theory. Mathematically, quantum fields are formalized as operator-valued distributions. Although there is no direct method of measuring the fields themselves, the framework asserts that all particles are "excitations" of these fields. For example: whereas Maxwell's theory of classical electromagnetism describes light as a self-propagating wave in the electromagnetic field, in quantum electrodynamics light is the massless gauge boson particle called the "photon." Furthermore, the number of particles in an isolated system need not be conserved; an example of a process for which this is the case is bremsstrahlung. A heuristic for suggesting particles may be created and destroyed is found in Albert Einstein's famous equation formula_1, which asserts that energy and matter may in principle be exchanged. A more detailed understanding of the framework is obtained by studying the Lagrangian density of a field theory which encodes the information of its allowed particle interactions.