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Process in quantum mechanical theories
In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries
Canonical_quantization
Topics referred to by the same term
processing) Color quantization Vector quantization Quantization (music) Quantization (physics) Canonical quantization Geometric quantization Discrete spectrum
Quantization
Theoretical framework in physics
field (one with no interactions with matter) was developed via canonical quantization by treating the electromagnetic field as a set of quantum harmonic
Quantum_field_theory
Formulation of general relativity
so-called canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac.[3] Dirac's approach allows the quantization of systems
Canonical_quantum_gravity
Formulation of the quantum many-body problem
quantum many-body systems. In quantum field theory, it is known as canonical quantization, in which the fields (typically as the wave functions of matter)
Second_quantization
Converting classical mechanics to quantum mechanics
written in the canonical coordinates that are compatible with the Euclidean coordinates of standard classical mechanics. First quantization is appropriate
First_quantization
Pictorial representation of the behavior of subatomic particles
function of a quantum mechanical or statistical field theory. Within the canonical formulation of quantum field theory, a Feynman diagram represents a term
Feynman_diagram
Continuous progression from past to future
acceleration of the observer. Time quantization refers to the theory that time has a smallest possible unit. Time quantization is a hypothetical concept. In
Time
Systematic procedure of turning a classical theory into a quantum one
generalization involving infinite degrees of freedom is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field
Quantization_(physics)
Relation satisfied by conjugate variables in quantum mechanics
delta. Canonical quantization is applied, by definition, on canonical coordinates. However, in the presence of an electromagnetic field, the canonical momentum
Canonical commutation relation
Canonical_commutation_relation
Theory of quantum gravity merging quantum mechanics and general relativity
{{\tilde {E}}_{i}^{3}{\tilde {E}}^{3i}}}.} According to the rules of canonical quantization the triads E ~ i 3 {\displaystyle {\tilde {E}}_{i}^{3}} should be
Loop_quantum_gravity
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
Formulation of quantum mechanics
formalism of canonical quantization. Unlike previous methods, the path integral allows one to easily change coordinates between very different canonical descriptions
Path_integral_formulation
Sets of coordinates on phase space which can be used to describe a physical system
Symplectomorphism Kinetic momentum Complementarity (physics) Canonical quantization Canonical quantum gravity Goldstein, Herbert; Poole, Charles P. Jr.;
Canonical_coordinates
Physical theory with fields invariant under the action of local "gauge" Lie groups
theory. Quantization schemes intended to simplify such computations (such as canonical quantization) may be called perturbative quantization schemes.
Gauge_theory
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
Description of gravity using discrete values
today constructed in several versions. One version starts with the canonical quantization of general relativity. The analogue of the Schrödinger equation
Quantum_gravity
Interpretation of quantum mechanics
action in combination with a quantization prescription. This quantization prescription can be compared to canonical quantization and the path integral formulation
Stochastic_quantum_mechanics
Theory of gravitation as curved spacetime
consistent theory of quantum gravity. Another approach starts with the canonical quantization procedures of quantum theory. Using the initial-value-formulation
General_relativity
Differential algebra
of quantum mechanics and the process of canonical quantization. Consider a classical phase space with canonical coordinates ( q 1 , p 1 , … , q n , p n
Weyl_algebra
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
Description of a quantum-mechanical system
quantum mechanics can be appreciated in a single dimension. In canonical quantization, the classical variables x {\displaystyle x} and p {\displaystyle
Schrödinger_equation
Parameter describing the strength of a force
applies to some formulations of quantum field theory, in particular, canonical quantization in the interaction picture. In other formulations, the same event
Coupling_constant
Topological quantum field theory
Schwimmer, Adam; Seiberg, Nathan (30 October 1989). "Remarks on the canonical quantization of the Chern-Simons-Witten theory". Nuclear Physics B. 326 (1):
Chern–Simons_theory
Standard or referential form
states of the system Canonical quantum gravity, an attempt to quantize the canonical formulation of general relativity Canonical stress–energy tensor
Canonical
German and British mathematician and physicist
and British mathematician and theoretical physicist, pioneer of canonical quantization of field theories. Paul Weiss was born in Sagan in the German part
Paul_Weiss_(mathematician)
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
Lowest energy state in quantum electrodynamics
discussion see, Compagno, G.; Passante, R.; Persico, F. (2005). "§2.1 Canonical quantization in the Coulomb gauge". Atom-Field Interactions and Dressed Atoms
QED_vacuum
Symmetry of spatially mirrored systems
the action is invariant and the quantization is also invariant. For simplicity we will assume that canonical quantization is used; the vacuum state is then
Parity_(physics)
infinite set of harmonic oscillators, and by then utilizing the canonical quantization procedure to these oscillators; their paper was published in 1926
History of quantum field theory
History_of_quantum_field_theory
Conjecture on zeros of the zeta function
i H ^ {\displaystyle 1/2+i{\hat {H}}} . This is in contrast to canonical quantization, which leads to the Heisenberg uncertainty principle σ x σ p ≥ ℏ
Riemann_hypothesis
Superstring quantization approach
various ways to quantize the string within this framework including light-cone quantization, old canonical quantization, and BRST quantization. A consistent
RNS_formalism
Recipe for constructing a quantum analog of a classical physical theory
quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization
Geometric_quantization
Field theory of scalar fields
quantum scalar field theory is detailed in the canonical quantization article, which relies on canonical commutation relations among the fields. Essentially
Scalar_field_theory
Nonlinear form of the Schrödinger equation
Schrödinger field. Conversely, when the classical Schrödinger field is canonically quantized, it becomes a quantum field theory (which is linear, despite the
Nonlinear Schrödinger equation
Nonlinear_Schrödinger_equation
whom "Quantization problems suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations
Symplectic_category
Operation in Hamiltonian mechanics
transformations, called canonical transformations, which map canonical coordinate systems into other canonical coordinate systems. A "canonical coordinate system"
Poisson_bracket
Technique in computational 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
Physics principle formulated by Niels Bohr
}}[{\hat {A}},{\hat {B}}].} By this correspondence, now called canonical quantization, Dirac showed how the mathematical form of classical mechanics could
Correspondence_principle
Hypothetical quantum cosmological effect
the deviation of a loop quantized black hole from Hawking radiation. A novel observable quantum effect of black hole quantization is introduced. Shapiro
Hawking_radiation
Coordinate transformation that preserves the form of Hamilton's equations
In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p) → (Q, P) that preserves the form of Hamilton's equations
Canonical_transformation
Particle with opposite charges
upon the ideas, language and notation of canonical quantization of a quantum field theory. One may try to quantize an electron field without mixing the annihilation
Antiparticle
Mathematical structures that allow quantum mechanics to be explained
expresses them through Poisson brackets, a procedure now known as canonical quantization. Already before Schrödinger, the young postdoctoral fellow Werner
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Key result in Hamiltonian mechanics and statistical mechanics
quantum mechanics describes the time evolution of a mixed state. Canonical quantization yields a quantum-mechanical version of this theorem, the von Neumann
Liouville's theorem (Hamiltonian)
Liouville's_theorem_(Hamiltonian)
Dutch theoretical physicist
1088/0264-9381/9/5/015. hdl:1874/4627. S2CID 250821900. 't Hooft, G. (1993). "Canonical quantization of gravitating point particles in 2+1 dimensions". Classical and
Gerard_'t_Hooft
Quantization method for constrained Hamiltonian systems with second-class constraints
constraints in Hamiltonian mechanics, and to thus allow them to undergo canonical quantization. It is an important part of Dirac's development of Hamiltonian mechanics
Dirac_bracket
Topics referred to by the same term
album by The Original 7ven, the band formerly known as The Time Canonical quantization or vacuum expectation value, in quantum field theory Bose–Einstein
Condensate
Variety of resonant circuit
}^{t}V(\tau )d\tau } Since charge and flux are canonically conjugate variables, one can use canonical quantization to rewrite the classical hamiltonian in the
Quantum_LC_circuit
Basis of a type of algebraic structure
quantum groups introduced by Lusztig. The canonical basis for the irreducible representations of a quantized enveloping algebra of type A D E {\displaystyle
Canonical_basis
Mapping between functions in the quantum phase space
Weyl quantization. It is now understood that Weyl quantization does not satisfy all the properties one would require for consistent quantization and therefore
Wigner–Weyl_transform
Field equation for spin-3/2 fermions
}-ieA_{\mu }.} Johnson and Sudarshan found an inconsistency in the canonical quantization of the minimally coupled spin-3/2 field, and Velo and Zwanziger
Rarita–Schwinger_equation
Theorem in string theory
Hermitian structure of V is transferred to the image under quantization. The bosonic string quantization functors described here can be applied to any conformal
Goddard–Thorn_theorem
Vector used in astronomy
Upon canonical quantization, this invariant allows the energy levels of hydrogen-like atoms to be derived using only quantum mechanical canonical commutation
Laplace–Runge–Lenz_vector
Overview of mechanics based on the least action principle
bracket is replaced by the commutator of operators via Dirac's canonical quantization: { A , B } → 1 i ℏ [ A ^ , B ^ ] . {\displaystyle \{A,B\}\rightarrow
Analytical_mechanics
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
Group in mathematical representation theory
Bibcode:2006math.....10818G Gurevich, Shamgar; Hadani, Ronny (2005), Canonical quantization of symplectic vector spaces over finite fields, arXiv:0705.4556
Metaplectic_group
Formulation of general relativity
Ashtekar variables, which were a new canonical formalism of general relativity, raised new hopes for the canonical quantization of general relativity and eventually
Self-dual_Palatini_action
Formalism in classical field theory based on Hamiltonian mechanics
space, and where canonical coordinates are field functions at some instant of time. This Hamiltonian formalism is applied to quantization of fields, e.g
Hamiltonian_field_theory
Quantum feature of condensed-matter systems
generalized it to other systems like superconductivity. In terms of canonical quantization, the one-body density matrix can be written as ρ ( r , r ′ ) = ⟨
Off-diagonal_long-range_order
Description of gauge theories using loop operators
{{\tilde {E}}_{i}^{3}{\tilde {E}}^{3i}}}.} According to the rules of canonical quantization we should promote the triads E ~ i 3 {\displaystyle {\tilde {E}}_{i}^{3}}
Loop representation in gauge theories and quantum gravity
Loop_representation_in_gauge_theories_and_quantum_gravity
others and is often considered to be one of the pioneering ideas in canonical quantization. To motivate the general definitions, a definition is first formulated
System_of_imprimitivity
Generalization of Hamiltonian mechanics involving multiple Hamiltonians
helicity. From the view point of Zariski quantization, Takhtajan et al. propose quantization of Nambu dynamics. Quantizing Nambu dynamics leads to intriguing
Nambu_mechanics
Type of quantum field
two, only the photon field can be quantized using the conventional methods of canonical or path integral quantization. This has led to the theory of quantum
Bosonic_field
Type of field appearing in the Lagrangian
{H}}} . From now on we drop the hat and the asterisk. Remember that canonical quantization states ϕ ∼ ( a † + a ) {\displaystyle \phi \sim (a^{\dagger }+a)}
Source_field
Formulations of electromagnetism
gauge has the advantage of the equations being Lorentz invariant. Canonical quantization of the electromagnetic fields proceeds by elevating the scalar and
Mathematical descriptions of the electromagnetic field
Mathematical_descriptions_of_the_electromagnetic_field
Isomorphism of symplectic manifolds
Hilbert spaces are called quantizations. When the Lie group is the one defined by a Hamiltonian, it is called a "quantization by energy". The corresponding
Symplectomorphism
Quantization of cyclotron orbits
quantization contributes towards magnetic susceptibility of metals, known as Landau diamagnetism. Under strong magnetic fields, Landau quantization leads
Landau_levels
Semi-classical method for computing quantum eigenvalues
eigenvalues in quantum-mechanical systems. EBK quantization is an improvement from Bohr–Sommerfeld quantization which did not consider the caustic phase jumps
Einstein–Brillouin–Keller method
Einstein–Brillouin–Keller_method
Method of solution for certain mechanical problems
{\displaystyle \hbar } . Einstein's insight in the EBK quantization into the difficulty of quantizing non-integrable systems was based on this fact. Action-angle
Action-angle_coordinates
dimension of quantization. In one-dimensional quantization, dislons behave as bosonic quasiparticles. However, in three-dimensional quantization, the topological
Dislon
Conserved physical quantity; rotational analogue of linear momentum
subshells in chemistry is significantly affected by the quantization of angular momentum. Quantization of angular momentum was first postulated by Niels Bohr
Angular_momentum
Numerical coefficient in loop quantum gravity
S2CID 8417388. Ansari, Mohammad H. (2007). "Spectroscopy of a canonically quantized horizon". Nuclear Physics B. 783 (3): 179–212. arXiv:hep-th/0607081
Immirzi_parameter
Heat from a current in an electric conductor
particles collide with the quasi-particles in the conductor (i.e. the canonically quantized, ionic lattice oscillations in the harmonic approximation of a crystal)
Joule_heating
Technique in computational 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 computational methods
Light-front_computational_methods
Conceptual conflict between general relativity and quantum mechanics
evolution, not a constraint. Reduced phase-space quantization constraints are solved first and then quantized. This approach was considered for some time to
Problem_of_time
Electromagnetic effect in physics
resistance was exactly quantized. For this finding, von Klitzing was awarded the 1985 Nobel Prize in Physics. A link between exact quantization and gauge invariance
Quantum_Hall_effect
Approach to quantum theory
equations of motion and the quantization conditions (commutation relations) for a quantum field theory. Unlike the canonical formalism, which postulates
Schwinger's quantum action principle
Schwinger's_quantum_action_principle
The quantized state systems (QSS) methods are a family of numerical integration solvers based on the idea of state quantization, dual to the traditional
Quantized state systems method
Quantized_state_systems_method
ensemble Canonical probability distribution Canonical quantization Canonical quantum gravity Canonical transformation Capacitance Capacitance electroscope
Index_of_physics_articles_(C)
Field equation from quantum gravity
\operatorname {tr} ((g^{-1}dg)^{2})-(\operatorname {tr} (g^{-1}dg))^{2}.} Quantization "puts hats" on the momenta and field variables; that is, the functions
Wheeler–DeWitt_equation
Symmetry breaking through the vacuum state
general framework for describing such states. The ferromagnet is the canonical system that spontaneously breaks the continuous symmetry of the spins
Spontaneous_symmetry_breaking
Overview of and topical guide to machine learning
for vector output Kernel principal component analysis Learning vector quantization Leabra Linde–Buzo–Gray algorithm Local outlier factor Logic learning
Outline_of_machine_learning
If one then wished to canonically quantize this system, then one need promote the canonical Dirac brackets, not the canonical Poisson brackets to commutation
First-class_constraint
Second order recursive digital linear filter
High-order infinite impulse response filters can be highly sensitive to quantization of their coefficients, and can easily become unstable. This is much less
Digital_biquad_filter
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
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 of quantum mechanics
mathematical offshoots such as Kontsevich's deformation-quantization (see Kontsevich quantization formula) and noncommutative geometry.[citation needed]
Phase-space_formulation
Idealization of a large number of atomic-sized systems
particles with its environment) in order to stay in statistical equilibrium. Canonical ensemble (or NVT ensemble)—a statistical ensemble where the energy is
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
American theoretical physicist
has worked on the canonical approach to quantum gravity, lower-dimensional models of quantum gravity, issues related to quantization of diffeomorphism-invariant
Donald_Marolf
Numerical method in quantum field theory
M {\displaystyle \mathbb {R} \times M} . The g=0 theory can be canonically quantized, which endows the field ϕ {\displaystyle \phi } with a mode decomposition
Hamiltonian_truncation
Specific quantum state of a quantum harmonic oscillator
mathematical physics and in applied mathematics, with applications ranging from quantization to signal processing and image processing (see Coherent states in mathematical
Coherent_state
German astrophysicist (born 1931)
265–270, 284–287. Kundt spacetime pp-wave spacetime Kundt, W.: Canonical Quantization of Gauge Invariant Field Theories, SPRINGER TRACTS IN MODERN PHYSICS
Wolfgang_Kundt
Aspect of astrophysics history
way, made possible to pursue quantization of it using well-known techniques from quantum gauge field theory. The quantization of gravity in the Ashtekar
History of loop quantum gravity
History_of_loop_quantum_gravity
Technique to compress data
and multimedia codecs such as JPEG and MP3 have a front-end model and quantization followed by the use of prefix codes; these are often called "Huffman
Huffman_coding
Statistical description for the behavior of fermions
Italian). 3: 145–9., translated as Zannoni, Alberto (1999-12-14). "On the Quantization of the Monoatomic Ideal Gas". arXiv:cond-mat/9912229. Dirac, Paul A.
Fermi–Dirac_statistics
Mathematical theorem
any one of a number of different formulations of the uniqueness of the canonical commutation relations between position and momentum operators. It is named
Stone–von_Neumann_theorem
space quantization, also known as Moyal quantization, largely avoids the use of operators for quantum mechanical observables prevalent in the canonical formulation
José_Enrique_Moyal
Iranian physicist
doi:10.1063/1.2435646. - Ansari, M. H. (2007). "Spectroscopy of a canonically quantized horizon". Nucl. Phys. B. 783 (3): 179–212. arXiv:hep-th/0607081
Mohammad_H._Ansari
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
CANONICAL QUANTIZATION
CANONICAL QUANTIZATION
Surname or Lastname
English
English : from a Middle English personal name or nickname. The personal name existed in Old English, and is probably derived from Old English prim ‘early morning’ (from Latin primus ‘first’, used as the name of one of the canonical hours). The surname may be derived from this word as a Middle English nickname in the sense ‘fine’, ‘excellent’.French : feminine form of Prim 3.Dutch : variant of Priem.Probably an Americanized spelling of German Preim, a topographic name (of Slavic origin), perhaps from a river near Hannover; or of Preime, a variant of Primus.
Surname or Lastname
Irish
Irish : Anglicized form of Gaelic Mac Canann or Ó Canann (Ulster), or Ó Canáin (County Galway) ‘son (Mac) or descendant (Ó) of Canán’, a personal name derived from cano ‘wolf cub’. In Ulster it may also be from Ó Canannáin ‘descendant of Canannán’, a diminutive of the personal name.English : from Middle English canun ‘canon’ (Old Norman French canonie, canoine, from Late Latin canonicus). In medieval England this term denoted a clergyman living with others in a clergy house; the surname is mostly an occupational name for a servant in a house of canons, although it could also be a nickname or even a patronymic.
CANONICAL QUANTIZATION
CANONICAL QUANTIZATION
Boy/Male
Indian, Punjabi, Sikh
Pray
Boy/Male
Tamil
Devadyumna | தேவாதà¯à®¯à¯à®®à®¨à®¾
Glory of the gods
Girl/Female
Biblical American Greek
Green herb.
Boy/Male
Hindu
Prince
Female
Scandinavian
Short form of Scandinavian Susanna, SANNA means "lily."
Boy/Male
British, English
God is My Strengh
Boy/Male
Shakespearean
Pericles, Prince of Tyre' Servant to the Pander.
Girl/Female
Indian
Goddess Lakshmi, The Goddess who has the divine wheel
Girl/Female
Arabic
Gift
Female
Hindi/Indian
(शकà¥à¤¨à¥à¤¤à¤²à¤¾) Hindi name SHAKUNTALA means "bird." In mythology, this is the name of the mother of Emperor Bharata.
CANONICAL QUANTIZATION
CANONICAL QUANTIZATION
CANONICAL QUANTIZATION
CANONICAL QUANTIZATION
CANONICAL QUANTIZATION
v. t.
To deprive of canonical authority.
a.
Chronic.
a.
Pertaining to Aaron, the first high priest of the Jews.
a.
Alt. of Cannonical
n.
A cannibal.
adv.
In a canonical manner; according to the canons.
a.
Alt. of Aaronical
a.
One of the canonical books of the Old Testament.
a.
Plane or flat on one side, and conical on the other.
a.
Laconian; characteristic of, or like, the Spartans; hence, stern or severe; cruel; unflinching.
a.
Of or pertaining to husbandmen.
n.
The quality of being canonical; canonicity.
a.
Having the form of, or resembling, a geometrical cone; round and tapering to a point, or gradually lessening in circumference; as, a conic or conical figure; a conical vessel.
n. pl.
The dress prescribed by canon to be worn by a clergyman when officiating. Sometimes, any distinctive professional dress.
a.
See Laconic, a.
a.
Expressing much in few words, after the manner of the Laconians or Spartans; brief and pithy; brusque; epigrammatic. In this sense laconic is the usual form.
a.
Alt. of Laconical
n.
The office of a canon; a canonry.
a.
Of or pertaining to a canon; established by, or according to a , canon or canons.
a.
Slightly conical.