We consider an approach in which the usual wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation of mode $j$ of the electromagnetic field is further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j}).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schr\"odinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.We consider an approach in which the usual wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation of mode $j$ of the electromagnetic field is further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j}).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schr\"odinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.

arXiv:2103.00596Physical Review ADec 1, 20213 citations

ON THE PARTICLE PICTURE OF QUANTIZED BOSE FIELDS. PART I

J. Leite Lopes

Mar 31, 19510 citations

Counting the Uncountable: A Narrative Review of Second Quantization and Feynman Diagrams, from Dirac's Oscillators to the Many-Body Problem

Zen Revista, 10 PHYSICS

Second quantization and its diagrams are field theory's working language: the occupation-number formalism—Dirac's 1927 quantized radiation, Jordan and Wigner's anticommuting fermions, Fock's space—that makes variable particle number natural, and the Feynman diagrams—the space-time pictures of 1949 whose algebra Dyson unified—that make perturbation theory drawable. This article presents a narrative review of the primary literature that built that language, from Dirac's 1927 emission and absorption quantization, Jordan and Wigner's 1928 Pauli equivalence, and Fock's 1932 configuration space, through the QED reconstruction of Tomonaga's 1946 invariant formulation, Schwinger's 1948 magnetic moment, Feynman's 1949 theory of positrons and space-time approach, and Dyson's 1949 unification, Feynman's 1962 lecture volume, Mattuck's 1976 guide to the many-body diagrams, Peskin and Schroeder's 1995 introduction, and Coleman's 2015 many-body synthesis. The synthesis is organized around three themes: the occupation-number settlement, in which variable particle number became formalism—bosonic commutators, fermionic anticommutators, Fock's space; the diagrammatic revolution, in which QED's infinities were organized into pictures with rules—and measured; and the many-body expansion, in which the same diagrams described solids, fluids, and superconductors. It is concluded that second quantization's genius is bookkeeping—particles as excitations—and that the diagrams are the bookkeeping's pictures: perturbation theory made visible, its rules the field's grammar.Second quantization and its diagrams are field theory's working language: the occupation-number formalism—Dirac's 1927 quantized radiation, Jordan and Wigner's anticommuting fermions, Fock's space—that makes variable particle number natural, and the Feynman diagrams—the space-time pictures of 1949 whose algebra Dyson unified—that make perturbation theory drawable. This article presents a narrative review of the primary literature that built that language, from Dirac's 1927 emission and absorption quantization, Jordan and Wigner's 1928 Pauli equivalence, and Fock's 1932 configuration space, through the QED reconstruction of Tomonaga's 1946 invariant formulation, Schwinger's 1948 magnetic moment, Feynman's 1949 theory of positrons and space-time approach, and Dyson's 1949 unification, Feynman's 1962 lecture volume, Mattuck's 1976 guide to the many-body diagrams, Peskin and Schroeder's 1995 introduction, and Coleman's 2015 many-body synthesis. The synthesis is organized around three themes: the occupation-number settlement, in which variable particle number became formalism—bosonic commutators, fermionic anticommutators, Fock's space; the diagrammatic revolution, in which QED's infinities were organized into pictures with rules—and measured; and the many-body expansion, in which the same diagrams described solids, fluids, and superconductors. It is concluded that second quantization's genius is bookkeeping—particles as excitations—and that the diagrams are the bookkeeping's pictures: perturbation theory made visible, its rules the field's grammar.

Aug 30, 20260 citations

Particle Position in Quantum Field Theories

WORLD SCIENTIFIC eBooksApr 1, 20200 citations

Two slit interference-classical and quantum pictures

D.G.C. Jones

Young's double-slit experiment demonstrates clearly the propagation of light in the form of a wave motion. Common attempts at a quantized picture of the experiment tend to describe light in terms of the propagation of small spatially localized particles. This is wrong, and unnecessary if quantization of the electric and magnetic field vectors is considered properly. Interference between normal modes of the field is a straightforward result in both classical and quantized pictures. Such an approach sheds more light on the quantization process and on topics of interest in modern optics.Young's double-slit experiment demonstrates clearly the propagation of light in the form of a wave motion. Common attempts at a quantized picture of the experiment tend to describe light in terms of the propagation of small spatially localized particles. This is wrong, and unnecessary if quantization of the electric and magnetic field vectors is considered properly. Interference between normal modes of the field is a straightforward result in both classical and quantized pictures. Such an approach sheds more light on the quantization process and on topics of interest in modern optics.

European Journal of PhysicsJul 1, 199417 citations

We consider an approach in which the usual wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation of mode

j

of the electromagnetic field is further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j}).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schr\"odinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.