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Formulation of the quantum many-body problem
Canonical quantization First quantization Geometric quantization Quantization (physics) Schrödinger functional Scalar field theory Second quantization on Wikiversity
Second_quantization
Process in quantum mechanical theories
theory context, it is also called the second quantization of fields, in contrast to the semi-classical first quantization of single particles. When it was
Canonical_quantization
Converting classical mechanics to quantum mechanics
First quantization is a procedure for converting equations of classical particle equations into quantum wave equations. The companion concept of second quantization
First_quantization
Quantization giving rise to photons
The quantization of the electromagnetic field is a procedure in physics turning Maxwell's classical electromagnetic waves into particles called photons
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Quasiparticle of mechanical vibrations
mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves
Phonon
Model of electronic band structures of solids
understood by working under a second quantization formalism. Using the atomic orbital as a basis state, the second quantization Hamiltonian operator in the
Tight_binding
Force resulting from the quantisation of a field
field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength
Casimir_effect
Type of machine learning model
preserving most of its performance. Quantization can be further classified as static quantization if the quantization parameters are determined beforehand
Large_language_model
that the non-conservation of fermion species is a consequence of second quantization. Creation and annihilation of fermions came to the fore, and it was
History of quantum field theory
History_of_quantum_field_theory
Formalism in string theory
classical action found by second-quantizing the free string and adding interaction terms. As is usually the case in second quantization, a classical field configuration
String_field_theory
Elementary particle or quantum of light
electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory;
Photon
Formulation to quantize gauge field theories in physics
relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT)
BRST_quantization
Anticommutating number
physics. Specifically, in quantum field theory, or more narrowly, second quantization, one works with ladder operators that create multi-particle quantum
Grassmann_number
Interference effect of two photons
timing. Since this effect relies on the existence of photons and the second quantization, it can not be fully explained by classical optics. The effect provides
Hong–Ou–Mandel_effect
Field theory of scalar fields
complications, scalar fields are often the easiest to appreciate second quantization through. For this reason, scalar field theories are often used for
Scalar_field_theory
Multi particle state space
"Konfigurationsraum und zweite Quantelung" ("Configuration space and second quantization"). Informally, a Fock space is the sum of a set of Hilbert spaces
Fock_space
Electromagnetic radiation humans can see
as excitations of quantum fields, a process with the misnomer of second quantization. And at the end of the 1940s a full theory of quantum electrodynamics
Light
Operators useful in quantum mechanics
the use of these operators instead of wavefunctions is known as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators
Creation and annihilation operators
Creation_and_annihilation_operators
Predecessor to modern quantum mechanics (1900–1925)
orientations, so that the process of quantization does not pick out a preferred axis. For this reason, the name "space quantization" fell out of favor, and the
Old_quantum_theory
American theoretical physicist, futurist and author
theory and quantum field theory. An explicit description of the second-quantization of the light-cone string was given by Kaku and Keiji Kikkawa. Kaku
Michio_Kaku
Quantum mechanics mathematical equation
The above expression is true for any kind of operators. (see also Second quantization) Green–Kubo relations Kubo, Ryogo (1957). "Statistical-Mechanical
Kubo_formula
Number-state in quantum mechanics
physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics. The particle representation was
Fock_state
Mathematical mapping in quantum mechanics
Wayback Machine. Archived from the original (PDF) on 2019-11-03. Coleman, Piers. "Simple Examples of Second Quantization" (PDF). University of Chicago.
Jordan–Wigner_transformation
Electronic structure method
_{y}=|m,n+1\rangle \langle m,n|e^{i\theta _{m,n}^{y}}} and in the second quantization formulation T x = ψ m + 1 , n † ψ m , n e i θ m , n x , T y = ψ m
Peierls_substitution
Background energy existing in space
field in question. The second quantization of quantum field theory requires that each such ball–spring combination be quantized, that is, that the strength
Vacuum_energy
Continuous progression from past to future
down in the figure depending on the acceleration of the observer. Time quantization is a hypothetical concept that time has a smallest possible unit. In
Time
Theory in physics about the nature of light
are explained as excitations of the electromagnetic field using second quantization. Corpuscularianism Speed of gravity Photon Philosophy of physics
Corpuscular_theory_of_light
Fermion that is its own antiparticle
mathematically in terms of the creation and annihilation operators of second quantization: The creation operator γ j † {\displaystyle \gamma _{j}^{\dagger
Majorana_fermion
Multiplicative function in number theory
"primons" have energies log ( p ) {\displaystyle \log(p)} . Under second quantization, multiparticle excitations are considered; these are given by log
Möbius_function
Branch of chemistry
number of constituents. It is based on quantum physics – mostly second quantization formalism – and quantum electrodynamics. Hence, theoretical chemistry
Theoretical_chemistry
Theoretical framework in physics
systems. The process of quantizing an arbitrary number of particles instead of a single particle is often also called second quantization. The foregoing procedure
Quantum_field_theory
Model for topological superconductors in physics
temperature, subjected to nearest neighbour hopping interactions, given in second quantization formalism as H = − μ ∑ j = 1 N ( c j † c j − 1 2 ) + ∑ j = 1 N −
Kitaev_chain
Formulation of classical mechanics in terms of Hilbert spaces
1007/s40509-017-0113-2. ISSN 2196-5609. Schönberg, M. (1952). "Application of second quantization methods to the classical statistical mechanics". Il Nuovo Cimento
Koopman–von Neumann classical mechanics
Koopman–von_Neumann_classical_mechanics
Mathematical transform that expresses a function of time as a function of frequency
treated as a separate harmonic oscillator and then quantized, a procedure known as "second quantization". Fourier methods have been adapted to also deal
Fourier_transform
Model from mathematical physics
p ⟩ {\displaystyle |p\rangle } labelled by the prime numbers p. Second quantization gives a new Hilbert space K, the bosonic Fock space on H, where states
Primon_gas
geometric quantization, quantization commutes with reduction states that the space of global sections of a line bundle L satisfying the quantization condition
Quantization commutes with reduction
Quantization_commutes_with_reduction
Relativistic quantum mechanical wave equation
Dirac fermion wavefunction. In the second quantization form of quantum field theory the Dirac spinor is quantized to be an operator-valued spinor field
Dirac_equation
Operator in quantum mechanics
}\\[1ex]\end{array}}} Harmonic oscillator Quantum harmonic oscillator Second quantization Quantum field theory Thermodynamics (-1)F Bruus, Henrik; Flensberg
Particle_number_operator
Method for converting signals between digital and analog
feedback loop during quantization to the lower bit depth that continuously corrects quantization errors and moves quantization noise to higher frequencies
Delta-sigma_modulation
Quantum mechanical model
properties of the phonon are best understood using the methods of second quantization and operator techniques described elsewhere. In the continuum limit
Quantum_harmonic_oscillator
Simplified model in condensed matter physics
The second term is the on-site interaction of strength U {\displaystyle U} that represents the electron repulsion. Written out in second quantization notation
Hubbard_model
Physical law for entropy and heat
The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement
Second_law_of_thermodynamics
Hypothetical particle with one magnetic pole
charge quantization has appeared. (The concept of local gauge invariance—see Gauge theory—provides a natural explanation of charge quantization, without
Magnetic_monopole
Fields giving rise to fermionic particles
the result of having a Lorentz invariant integration measure. In second quantization, ψ ( x ) {\displaystyle \psi (x)} is promoted to an operator, so
Fermionic_field
Atomic model introduced by Niels Bohr in 1913
the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Wilson–Sommerfeld quantization condition
Bohr_model
Charge carried by one proton or electron
the electric constant, and ħ is the reduced Planck constant. Charge quantization is the principle that the charge of any object is an integer multiple
Elementary_charge
Describe the optical response of semiconductors
always in many-body physics, it is most convenient to apply the second-quantization formalism after the appropriate system Hamiltonian H ^ S y s t e
Semiconductor_Bloch_equations
Spectral density of light emitted by a black body
did not propose that light propagating in free space is quantized. The idea of quantization of the free electromagnetic field was developed later, and
Planck's_law
Optical device which splits a beam of light in two
quantum mechanics, the electric fields are operators as explained by second quantization and Fock states. Each electrical field operator can further be expressed
Beam_splitter
Representation of the symmetry group of spacetime in special relativity
equation are considered as classical fields prior to (second) quantization. While second quantization and the Lagrangian formalism associated with it is
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Quantization of cyclotron orbits
quantization contributes towards magnetic susceptibility of metals, known as Landau diamagnetism. Under strong magnetic fields, Landau quantization leads
Landau_levels
Raising and lowering operators
This wave equation can be represented using a second quantized approach, known as second quantization. The number of particles in each single-particle
Anti-symmetric_operator
deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich. Given a Poisson algebra (A, {⋅, ⋅}), a deformation quantization is
Kontsevich quantization formula
Kontsevich_quantization_formula
Raising and lowering operators in quantum mechanics
the quantum harmonic oscillator or the "number representation" of second quantization are just special cases of this fact. Ladder operators then become
Ladder_operator
Quantities describing probability of absorption or emission of light
be done easily, that of A coefficient requires using results of second quantization. This is because the theory developed by dipole approximation and
Einstein_coefficients
Spin 1 quasiparticle; quantum of a spin wave
further developed the quantitative theory of magnons, quantized spin waves. Using the second quantization formalism they showed that magnons behave as weakly
Magnon
Signal encoder
the quantized signal. The incorporation of the decoder inside the encoder allows quantization of the differences, including nonlinear quantization, in
Differential pulse-code modulation
Differential_pulse-code_modulation
Quantum algorithm
qubitize: that is to write the many-body Hamiltonian of the system using second quantization, and then use a mapping to write the creation-annihilation operators
Variational quantum eigensolver
Variational_quantum_eigensolver
Relativistic wave equation in quantum mechanics
breakdown of the single-particle interpretation of the theory. In the second quantization framework of quantum field theory, fields are elevated to be operators
Klein–Gordon_equation
Quantized unit of magnetic flux
from Φ0. The flux quantization is a key idea behind a SQUID, which is one of the most sensitive magnetometers available. Flux quantization also plays an important
Magnetic_flux_quantum
Wigner distribution function in physics as opposed to in signal processing
operators, in Weyl quantization. Thus, the Wigner function is the cornerstone of quantum mechanics in phase space. In second quantization the phase-space
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Integration for Grassmann variables
doi:10.1007/BF02745446. S2CID 122333001. A. Berezin, The Method of Second Quantization, Academic Press, (1966) Itzykson, Claude; Zuber, Jean Bernard (1980)
Berezin_integral
Electronic device
At the time, the photodetectors could only sense the one-dimensional quantization when the light traveled in parallel to the material layers, which typically
Quantum well infrared photodetector
Quantum_well_infrared_photodetector
Description of the ground state of a quantum system
approach to the weakly interacting Bose gas using the formalism of second quantization. The optical potential well V twist ( r , t ) = V twist ( z , r
Gross–Pitaevskii_equation
Nobel laureate theoretical chemist
Institutions Cornell University Thesis Theory of Polyhedral Molecules: Second Quantization and Hypochromism in Helices. (1962) Doctoral advisor William N. Lipscomb
Roald_Hoffmann
System that converts an analog signal into a digital signal
signal. The conversion involves quantization of the input, so it necessarily introduces a small amount of quantization error. Furthermore, instead of continuously
Analog-to-digital_converter
Ratio of the desired signal to the background noise
possible noise level is the error caused by the quantization of the signal, sometimes called quantization noise. This noise level is non-linear and signal-dependent;
Signal-to-noise_ratio
Model of interacting spinless bosons on a lattice
physics, the Bose–Hubbard Hamiltonian can be derived starting from the second quantized Hamiltonian that describes a gas of ultracold atoms in the optical
Bose–Hubbard_model
Number of bits of information recorded for each digital audio sample
determined by quantization error. The bit depth has no impact on the frequency response, which is constrained by the sample rate. Quantization error introduced
Audio_bit_depth
Identity in abelian theories due to gauge invariance
term. Gauge-fixing terms are required so as to be able to perform second quantization of a classical gauge theory. The path-integral (Lagrangian) formulation
Ward–Takahashi_identity
Turkish-American theoretical physicist (1926–1994)
Field Quantization 1985 Zitterbewegung of the Electron in External Fields 1986 Quantum Electrodynamics Based on Self-Energy versus Quantization of Fields
Asım_Orhan_Barut
High-temperature expansion in statistical mechanics
many-body physics or quantum optics, it is most convenient to apply the second-quantization formalism to describe the physics involved. For example, a light
Cluster_expansion
integration Berezin, Feliks Aleksandrovich (1966) [1965], The method of second quantization, Pure and Applied Physics, vol. 24, Boston, MA: Academic Press,
Berezinian
Non-perturbative approach to quantum field theory
Normal ordering of creation operators is useful when working in the second quantization formalism. A radial-ordered OPE can be written as a normal-ordered
Operator_product_expansion
Theorem in quantum mechanics
L. P.; Biedenharn, L. C. (1984). "Quaternion quantum mechanics: Second quantization and gauge fields". Annals of Physics. 157 (2): 432–488. Bibcode:1984AnPhy
Gleason's_theorem
Large language model by Meta AI
both tensors and metadata. The format focuses on supporting different quantization types, which can reduce memory usage, and increase speed at the expense
Llama_(language_model)
Extension of the Bohr model
the quantized angular momentum condition of the Bohr model with a radial quantization (condition by William Wilson, the Wilson–Sommerfeld quantization condition):
Bohr–Sommerfeld_model
Quantum mechanical operator related to rotational symmetry
{\displaystyle \hbar } is reduced Planck constant: A common way to derive the quantization rules above is the method of ladder operators. The ladder operators for
Angular_momentum_operator
Candidate unified theory of physics
ISSN 0944-2669. S2CID 54692714. Finster, Felix (2010). "Entanglement and second quantization in the framework of the fermionic projector". Journal of Physics
Causal_fermion_systems
Lossy compression method for reducing the size of digital images
domain, the process of reducing information is called quantization. In simpler terms, quantization is a method for optimally reducing a large number scale
JPEG
Physical theory with fields invariant under the action of local "gauge" Lie groups
variety of means. Methods for quantization are covered in the article on quantization. The main point to quantization is to be able to compute quantum
Gauge_theory
Chinese artificial intelligence company
in late September 2025 marked the first integration of FP8 and Int4 quantization on Cambricon chips. It also supports native FP8 on Moore Threads GPUs
Z.ai
Branch of physics
distribution function (fph). The photon Hamiltonian for the quantized radiation field (second quantization) is H p h = 1 2 ∫ ( ε o e e 2 + μ o − 1 b e 2 ) d V
Heat_transfer_physics
Method for approximating many-body systems
operator of all double excitations, and so forth. In the formalism of second quantization these excitation operators are expressed as T 1 = ∑ i ∑ a t a i a
Coupled_cluster
calculated the photon distribution for Blackbody radiation using the second quantization method, but with a composite photon. The atoms in the walls of the
Neutrino_theory_of_light
Soviet theoretical physicist (1921-1968)
development of operator form of perturbation theory, approximate second quantization, adiabatic approximation for systems with translational invariance
Sergei_Tyablikov
Particle effect
wavefunction for a nonrelativistic motion. It doesn't appear in the correct second quantized theory, or rather, it is resolved by using Feynman propagators and
Zitterbewegung
Clock that monitors the resonant frequency of atoms
June 2022. Retrieved 20 June 2022. Rabi, I. I. (15 April 1937). "Space Quantization in a Gyrating Magnetic Field". Physical Review. 51 (8): 652–654. Bibcode:1937PhRv
Atomic_clock
Quantization procedure in quantum field theory
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to
Light-front quantization applications
Light-front_quantization_applications
Hungarian theoretical chemist (born 1955)
chemist who is known for his research on application of the theory of second quantization in quantum chemistry. In 2016 a festschrift from Theoretical Chemistry
Péter_Surján
Digital representation of sampled analog signals
type of PCM in which the quantization levels are linearly uniform. This is in contrast to PCM encodings in which quantization levels vary as a function
Pulse-code_modulation
Microscopic interaction in metals
This term is responsible for the creation of Cooper pairs. Using second quantization, Bardeen–Pines interaction leads the Hamiltonian H ^ = ∑ k σ ε k
Bardeen–Pines_interaction
Speed of electromagnetic waves in vacuum
energy, supporting tight constraints in specific models of spacetime quantization on how this speed is affected by photon energy for energies approaching
Speed_of_light
Japanese polymer physicist
the original on 2015-07-12, retrieved 2013-03-01 Doi, M. (1976), "Second quantization representation for classical many-body system", J. Phys. A: Math
Masao_Doi
Canadian and American theoretical physicist
tensorial operators, which incorporated the methods of group theory and second quantization into shell-model theory. ... Through these methods, he derived sum
James_Bruce_French
Technique used to encode voices in telephony
differential pulse-code modulation (DPCM) that varies the size of the quantization step, to allow further reduction of the required data bandwidth for a
Adaptive differential pulse-code modulation
Adaptive_differential_pulse-code_modulation
Example of a phase-space star product in mathematics
to have emerged only in the 1970s, in homage to his flat phase-space quantization picture. The product for smooth functions f and g on R 2 n {\displaystyle
Moyal_product
with models of strongly correlated systems, providing a method to second-quantize valence fluctuations within a restrictive manifold of states. In the
Slave_boson
Physical constant in quantum mechanics
the Normal Spectrum" With this new condition, Planck had imposed the quantization of the energy of the oscillators, in his own words, "a purely formal
Planck_constant
German-born theoretical physicist (1879–1955)
Development of our Views on the Composition and Essence of Radiation"), on the quantization of light, and in an earlier 1909 paper, Einstein showed that Max Planck's
Albert_Einstein
SECOND QUANTIZATION
SECOND QUANTIZATION
Boy/Male
Scottish American
Second son.
Surname or Lastname
English
English : from Richward, a Norman personal name composed of the Germanic elements rīc ‘power(ful)’ + ward ‘guard’.French : from Old French record, recort ‘recollection’, ‘account’, ‘testimony’, and by extension ‘witness’, hence perhaps a nickname for someone who had given evidence in a court of law, or a metonymic occupational name for a clerk who recorded court proceedings.New England variant of French Ricard, reflecting an Americanized spelling of the Canadian pronunciation.
Girl/Female
Indian
Dual, Second
Boy/Male
Scottish American Irish Russian
Second son.
Boy/Male
Indian
Second
Boy/Male
African American American
Of man.
Male
English
Variant spelling of Middle English Estmond, ESMOND means "gracious protector."Â
Girl/Female
Muslim
Second Khalifah
Female
English
Anglicized form of Scottish Gaelic Seònaid, SEONA means "God is gracious."
Girl/Female
Tamil
Dual, Second
Girl/Female
Biblical
Second.
Girl/Female
Spanish
Lively.
Boy/Male
Scottish
Second son.
Girl/Female
Tamil
Second
Boy/Male
Christian & English(British/American/Australian)
Protective Grace
Surname or Lastname
English
English : from an Old English personal name composed of the elements ēast ‘grace’, ‘beauty’ + mund ‘protection’. This name was also used by the Norman, among whom it represents a continental Germanic cognate of the Old English name.
Boy/Male
English
Protected by God. Grace and protection. From the Old English name Estmund. Commonly used as a...
Boy/Male
American, British, Christian, English, French, German
Wealthy Protector; Protected by Grace; Gracious Protector
Female
English
From the name of the state of Arizona in the United States of America, a place considered sacred by the Native Americans. It was named after Sedona Miller Schnebly (1877-1950), the wife of the city's first postmaster. Meaning unknown.
Girl/Female
Indian
Second
SECOND QUANTIZATION
SECOND QUANTIZATION
Boy/Male
Arabic, Hindu, Indian, Marathi, Muslim, Sindhi
Perfect; Complete; Accomplished
Boy/Male
English, Gaelic, Scottish
Child of the Sea; Huge Mountain
Female
African
beautiful.
Girl/Female
Muslim
Intelligent, Judicious
Boy/Male
Sikh
Lamp of war
Girl/Female
Bengali, Indian
Creative Woman; Prayers for Others; Who Won Beauty
Girl/Female
Arabic, Muslim
Pure; Chaste; Fem; Sinless
Boy/Male
Tamil
Paramhans | பரமஹஂஸ
Sadguru
Boy/Male
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Master of the Earth
Girl/Female
Tamil
Sea shell, Oyster
SECOND QUANTIZATION
SECOND QUANTIZATION
SECOND QUANTIZATION
SECOND QUANTIZATION
SECOND QUANTIZATION
adv.
In the second place.
n.
A right of inheritance belonging to a second son; a property or possession so inherited.
imp. & p. p.
of Second
n.
The second part in a concerted piece.
n.
The second part in a concerted piece; -- often popularly applied to the alto.
a.
The sixtieth part of a minute of time or of a minute of space, that is, the second regular subdivision of the degree; as, sound moves about 1,140 English feet in a second; five minutes and ten seconds north of this place.
adv.
Secondly; in the second place.
a.
To follow or attend for the purpose of assisting; to support; to back; to act as the second of; to assist; to forward; to encourage.
n.
One who seconds or supports what another attempts, affirms, moves, or proposes; as, the seconder of an enterprise or of a motion.
a.
Of the rank or degree below the best highest; inferior; second-rate; as, a second-class house; a second-class passage.
a.
Having the power of second-sight.
n.
A secdond trial, experiment, or test; a second judicial trial, as of an accused person.
v. t.
A writing by which some act or event, or a number of acts or events, is recorded; a register; as, a record of the acts of the Hebrew kings; a record of the variations of temperature during a certain time; a family record.
prep.
Past, out of the reach or sphere of; further than; greater than; as, the patient was beyond medical aid; beyond one's strength.
a.
Of the second size, rank, quality, or value; as, a second-rate ship; second-rate cloth; a second-rate champion.
n.
That which is seen at a second view; a meaning beyond the literal sense; the second intention; a hidden signification.
a.
Cutting; divivding into two parts; as, a secant line.
v. t.
An official contemporaneous memorandum stating the proceedings of a court of justice; a judicial record.
a.
Being of the same kind as another that has preceded; another, like a protype; as, a second Cato; a second Troy; a second deluge.
n.
A unit for the measurement of small intervals of time, such that 1012 (ten trillion) of these units make one second.