# Quantization (physics)

**quantizationquantizedquantizequantizingquantisationbundles of energycanonical approach to quantum mechanicsenergy quantizationfield quantumminimum length**

In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.wikipedia

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### Quantum mechanics

**quantum physicsquantum mechanicalquantum theory**

In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. (It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics.

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to the precision with which quantities can be measured (the uncertainty principle).

### Quantum

**quantaquantizedquantal**

Also related is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance as light quanta).

The fundamental notion that a physical property may be "quantized" is referred to as "the hypothesis of quantization".

### Photon

**photonslight quantaincident photon**

Also related is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance as light quanta).

Although these semiclassical models contributed to the development of quantum mechanics, many further experiments beginning with the phenomenon of Compton scattering of single photons by electrons, validated Einstein's hypothesis that light itself is quantized.

### Field (physics)

**fieldfieldsfield theory**

(It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics. Quantization converts classical fields into operators acting on quantum states of the field theory. The classical field is treated as a dynamical variable called the canonical coordinate, and its time-derivative is the canonical momentum.

For example, quantizing classical electrodynamics gives quantum electrodynamics.

### Canonical quantization

**field operatorcanonicalfield operators**

The first method to be developed for quantization of field theories was canonical quantization.

In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible.

### BRST quantization

**BRSTBRST formalismBRST theory**

It involves the Batalin–Vilkovisky formalism, an extension of the BRST formalism.

In theoretical physics, the BRST formalism, or BRST quantization (where the BRST refers to Becchi, Rouet, Stora and Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry.

### Loop quantum gravity

**Loop gravitycovariant quantum gravityQuantum Graph Theory**

See Loop quantum gravity.

To do this, in LQG theory space and time are quantized analogously to the way quantities like energy and momentum are quantized in quantum mechanics.

### Quantum number

**quantum numbersq-number3d, 4d, and 5d**

An important aspect of quantum mechanics is the quantization of many observable quantities of interest.

### Path integral formulation

**path integralFeynman path integralpath integrals**

A quantum-mechanical description of the classical system can also be constructed from the action of the system by means of the path integral formulation.

Feynman showed that this formulation of quantum mechanics is equivalent to the canonical approach to quantum mechanics when the Hamiltonian is at most quadratic in the momentum.

### Quantum Hall effect

**von Klitzing constantquantum Hallinteger quantum Hall effect**

The integer quantization of the Hall conductance was originally predicted by University of Tokyo researchers Tsuneya Ando, Yukio Matsumoto and Yasutada Uemura in 1975, on the basis of an approximate calculation which they themselves did not believe to be true.

### First quantization

**semi-classicalturned into**

### Physics

**physicistphysicalphysicists**

In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.

### Quantum field theory

**quantum field theoriesquantum fieldquantum theory**

(It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics.

### Classical mechanics

**Newtonian mechanicsNewtonian physicsclassical**

(It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics.

### Electromagnetic field

**electromagnetic fieldselectromagneticEMF**

Also related is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance as light quanta).

### Particle physics

**high energy physicsparticle physicisthigh-energy physics**

This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

### Nuclear physics

**nuclear physicistnuclearnuclear science**

This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

### Condensed matter physics

**condensed matterCondensed matter theorycondensed-matter physics**

This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

### Quantum optics

**quantum electronicsquantum opticalquantum-optical**

### Quantum state

**eigenstatepure stateeigenstates**

Quantization converts classical fields into operators acting on quantum states of the field theory.

### Vacuum state

**quantum vacuumvacuumZero-point field**

The lowest energy state is called the vacuum state.

### Probability amplitude

**probability densityBorn probabilitytransition amplitude**

The reason for quantizing a theory is to deduce properties of materials, objects or particles through the computation of quantum amplitudes, which may be very complicated.

### Renormalization

**renormalizablerenormalisationrenormalized**

Such computations have to deal with certain subtleties called renormalization, which, if neglected, can often lead to nonsense results, such as the appearance of infinities in various amplitudes.

### Canonical coordinates

**conjugate momentacanonical momentumconjugate momentum**

The classical field is treated as a dynamical variable called the canonical coordinate, and its time-derivative is the canonical momentum.