Questions tagged [quantization]

Quantization refers to the procedure or methodology for replacing a classical system by a quantum system. If the question is about the quantized or discrete behavior of a phenomenon use the [tag:discrete] instead.

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Experimental verification of quantization

I understand quantization as a map from Symplectic Manifolds $M$ (either finite dimensional or not) to Hilbert Spaces $H$, along with a rule that attach to every function $F$ in $M$ a hermitian ...
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Gauge Symmetries as Redundancies vs Constraints

I am very confused by these two points of view. Consider a theory whose space of fields is $V$ and that has an action $S$. Thinking of a gauge symmetry as a redundancy is your description means that ...
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Why does a square root term make the quantisation of action difficult?

When going over my lecturer's notes on String Theory and trying to understand a particle as a theory of gravity in 1D, it is mentioned that the action $(1)$ is regularisation invariant, $$S=-m\...
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Name of concept: Replace classical variables by quantum operators

I feel like there was a name for this sleight of hand approach and I've been unsuccessfully trying to google it for a while. I think Heisenberg introduced it and it's basically "putting hats on all ...
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Non-relativisitc Quantization of Classical Fields

When quantizing a theory of one particle, we are used to taking the classical dynamical variable $\gamma:\mathrm{time}\to\mathrm{space}$, the trajectory in time, and replacing it with another, ...
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On quantization of relativistic quantum theory on curved space

In his book "Lectures on quantum mechanics", at the end of chapter 3, Dirac states that "it does not seem possible to fulfill the conditions which are necessary for building up a relativistic ...
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How do the electrons absorb energy in an discharge tube that is used for produce an emission spectrum?

When there's hydrogen in a discharged tube it produces an emission spectrum, emitting energy(photons). (Eg:-When an electron jumps from 3rd energy level to 1st energy level, the electron emits a ...
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Experimental tests of operator ordering

In quantization, we frequently run into ordering ambiguities. In general, this means that there can be inequivalent quantum theories corresponding to the same classical theory. Has there ever been an ...
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What do we mean by radial quantisation in CFT?

When we quantise QFT we do that in equal time slices. In CFT it is useful to use equal radius slices. Why is that the case? And what does it mean?
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General question about quantization procedure

As far as I understood, when we want to quantize a system, the procedure can be the following (but probably not the most general one): We start by writing down the Lagrangian of the system. We ...
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Planck's Hypothesis Derivation

Max Planck in 1900 used the quantisation of energy to explain black body radiation. Using what principles did he arrive at his final formula $E=nhv$?
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Why various molecules in an ideal gas at a particular temperature can have only quantized energies?

Why various molecules in an ideal gas at a particular temperature can have only quantized energies? Why can't they have the energies distributed in a continuous fashion? Following is an image taken ...
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Canonical Quantization: Hamiltonian limitations

Before performing a canonical quantization there are some features of the Hamiltonian that have to be taken into account. For example, the hamiltonian has to be symmetric in order to be self-adjoint. ...
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Quantising Classical Lagrangian

Suppose you have a system described by the following Lagrangian: $$L=(1-gq²)\dot{q}^2/2.$$ How would you quantize this theory? Do you need to symmetrize the Hamiltonian before promoting the ...
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Quantization of the Nambu bracket

The most simple quantum mechanical system consists of a canonical pair of operators $\{P, Q\}$ satisfying $$ P Q - Q P = i \hbar. $$ It is well known that there is a unique (modulo unitary maps) ...
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Can Newtonian gravity be quantized?

Today, nobody knows how GR is truly supposed to be married with QFT. As a result, the standard model as it is typically presented does not include gravity. Could it be modified to include Newtonian ...
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Einstein–Brillouin–Keller quantization rule, what does it really mean?

The Einstein–Brillouin–Keller method is a quantization rule going from classical mechanics to quantum mechanics, according to wikipedia: I have several question regarding the above description: what ...
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What's the difference between canonical quantization and second quantization?

I am wondering the difference between the canonical quantization and the second quantization in quantum field theory. For example, a harmonic chain, one can write down its lagrangian density $\...
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Single electron in conductive cavity

It is a basic result in electrostatics that a charge $q$ in an arbitrary cavity of an ideal conductor will generate a total charge $-q$ on the surface of the cavity in such a way that the electric ...
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Obstruction in quantization. Weyl Ordering

What is an obstruction in quantization? I've found that obstructions object of the study of a mathematical theory, previously concerned with homotopy. The problem is that to explain what an ...
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Creation and Annnihilator Operators: generality and meaning

I am studying my fisrst course in quantum mechanichs where we treated the example of the Harmonic Oscillator through the Weyl Heisenberg Spectrum Generating Algebra Method. In that context we ...
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Uniqueness in the path integral vs canonical quantisation

In quantum mechanics it is well known that if you have a Lagrangian $\mathcal{L}$ and you want to quantise it, there is no unique way of doing this. This is because when you construct the Hamiltonian $...
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The WKB approximation and the Cotangent bundle

When we say (see pag. 9 of Lectures on the Geometry of Quantization) that the image of the differential of the phase function lies in the level set of the classical Hamiltonian is it simply ...
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Quantization of Chiral Boson

I am trying to understand the edge modes of fractional quantum Hall(FQH) effect from ChernSmions theory picture. Chern-Simons action with a boundary along $y$ produces the following action $ \...
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Why is angular momentum always quantized irrespective of the system?

In general, the eigenvalues of the components of position $\vec{r}$ and momentum $\vec{p}$ are not quantized. Certainly, not quantized for a free particle. Is there a physical explanation of how is it ...
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Geometrical way to view discretization of energy in quantum mechanics. How commutation relation implies discreteness?

The relation from which discreteness in eigenvalue of the energy of bound state arises is $[x, p]=i\hbar$ followed by the rule that wavefunction should be normalizable. So my question is there a ...
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The origin of quantization

I will present a question which already is buzzing in my head for quite a time. Actually quantum physics developed as a interplay of empirical results and theoretical developments where it is ...
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What is the flux $\Phi$ enclosed by cyclotron orbit, which can express the quantization rule?

Suppose an electron (mass $m$, charge $e$) in the xy-plane with $B=(0,0,B)$ (The classical EOM result in circular orbit). Using the Bohr-Sommerfeld quantization rule we can find that $E_n = (n+1/2)\...
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Compactness and Quantization

So I was thinking today about when observables become "quantized", and came to the conclusion that every instance of quantization I've ever come across has come about from solving the Schrödinger ...
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An example of Hamiltonian which fails with canonical quantization

The Groenewold's theorem states that canonical quantization, regarded as a rule to replace $\{A,B\}$ by $\frac{1}{i\hbar}[A,B]$ is inconsistent for some 3rd order polynomials of canonical variables $p$...
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Photon energy comes in packets

From the HyperPhysics page on the Photoelectric Effect: According to the Planck hypothesis, all electromagnetic radiation is quantized and occurs in finite "bundles" of energy which we call photons....
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Is color charge quantized?

I was reading this stackexchange question, and found the answer to my question not totally answered. Clearly there is color and anti-color in analogy to electric charge, and color charge clearly ...
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Quantizing first class constraints

Let $\gamma$ denote a first class constraint. Then if there exists a function on phase space $f(q,p)$ for which the Poisson bracket with the constraint does not vanish $\lbrace f, \gamma\rbrace \neq 0$...
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Does string theory need operator formalism to quantize?

Can we really use path integral approach to quantize for (first-quantized) string theory? This question is motivated from the following fact: even though we can establish exact correspondence between ...
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Can you quantize Grassmann-even superfields in the same fashion as Boson fields?

In a related Phys.SE question about supersymmetric Lagrangian $$ \mathcal{L} = - \frac{1}{2} (\partial S)^2 - \frac{1}{2} (\partial P)^2 - \frac{1}{2} \bar{\psi} \partial\!\!\!/ \psi, $$ the fields $S$...
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Why do I need energy quantization to explain the blackbody spectrum? [duplicate]

I don't understand why the postulate of "Energy Quantization" is needed to explain the black body energy spectrum. I think it suffices to say that Energy is proportional to frequency. That statement ...
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Why does the SUSY vacuum energy vanish independently of the quantization scheme?

This question was inspired by the comments here. It is straightforward to show that the SUSY vacuum energy vanishes, $H|0 \rangle = 0$, using nothing but the SUSY algebra. For people who prefer a less ...
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Canonical quantization of time-dependent lagrangians

I have a lagrangian $$ L(x^{a}, \dot{x}^{a}, t), $$ which is non-degenerate, quadratic in the fields, and contains an explicit dependence on the evolution parameter $t$. If $L$ was time-independent,...
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Why does a photon have to be one wavelength? [closed]

I've found nothing on this topic. Everyone says a photon is one wavelength of whatever beam of energy it belongs to, but no one says why this needs to be the case. If anyone has an answer, I'd be glad ...
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Quantization and wave-particle dualism of light

I'm studying atomic spectras and got puzzled about light-quantization. I'll expose my effort to understand it so far. Blackbody radiation Around the year $1900$ Planck explained blackbody radiation ...
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Do we need Planck’s constant for second quantization?

The widely circulated folklore surrounding Planck’s constant $\hbar$ lends it an aura of importance. But could $\hbar$ be a constant of human convention which is dispensable? Does the unorthodox view ...
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Coset Spaces in Quantization

What is the motivation for the use of coset spaces within the context of integral quantization? My main confusion is with the fact that coset spaces are inherently linear algebraic and make sense to ...
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What would be in the Kernel of a Dequantization Map?

Consider forming a symplectic map between all the Hamiltonians on Hilbert Space and all the Hamiltonians on Phase Space. (I understand that taking the Converse of the Groenewold Van-Hove Theorem this ...
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What is the problem of non-pertubative quantisation?

In reading books about quantisation, there is (sometimes hidden) the claim, that quantisation is done using a pertubative approach. You look at the free field, find that it is essentially a sum of ...
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Values of magnetic quantum number and angular momentum

What is the motivation for the values of the magnetic quantum number $m_l$ to take values of $ -l, -l+1, \cdots , l $ where $l$ is the angular momentum number? The ladder operators for angular ...
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Mass operator in lightcone quantization

I am studying string theory following Tong's notes. When deriving the mass operator in covariant quantization, we can do the following: From the constraints $(\partial_+X)^2=(\partial_-X)^2=0$, we ...
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Hamiltonian in QM/QFT path integral being Wigner transformation (Weyl-symbol)? of Hamiltonian operator?

The question is inspired from the answer of Why path integral approach may suffer from operator ordering problem?. In the answer, it says below equation 5: where $H(q,p)$ denotes the Weyl-symbol ...
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Physical aspects of representations of $C^{*}$ algebras

Suppose I have a $C^{*}$ algebra $\mathcal{A}$ of quantum observables. I could have used deformation quantization to obtain it from the classical Poisson manifold, or I could've just guessed it – for ...
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Phase space with torus topology

Consider a particular compact 2D symplectic manifold $\mathcal{M}$ defined as follows: The topology of $\mathcal{M}$ is a 2-torus. Let $\theta$ and $\varphi$ be the coordinate patch on $\mathcal{M}$ ...
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Constructing Quantum Theories without Semiclassical Quantization

This question builds off of this previous question particularly the excellent answer by @Cosmas Zachos and the this document which he attached. Quantization whatever form it takes always seeks to ...

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