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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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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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Is there a first quantized approach to M theory? (Laymen)

I'm a laymen so please, go easy on me if this is a bad question. String theory can be approached in first quantization or second quantization. However, I'm not sure if the same applies to M theory. ...
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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? Is the unorthodox view in ...
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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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1answer
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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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Are free electrons truly free?

As this diagram shows, energy levels get closer together as they get higher. Is a free electron then truly free? Or is it in such a high (bound) state of energy that the transitions become nearly (but ...
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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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1answer
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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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Why aren't the energy levels of the Earth quantized?

The Hamiltonian of the Earth in the gravity field of the Sun is the same as that of the electron in the hydrogen atom (besides some constants), so why are the energy levels of the Earth not quantized?...
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Some question about quantization of LC -Circuit and transmission line resonator

In this post @DanielSank left a good answer about Lagrangian method for an LC-Circuit. But for me is not clear the next things: When he wrote the equation for current and voltage according ...
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Deriving the Old Quantum Condition ($\oint p_i dq_i=nh$)

A body undergoing periodic motion in an orbit of quantum number $n$ will have a period $T$, determined by $$T=\oint \frac{ds}{v}=\oint \frac{ds}{\sqrt{\frac{2}{m}(E-V)}}$$ Where $ds$ is an ...
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Clarification about Heisenberg’s 1925 paper and the Bohr-Sommerfeld rule

I am reading Heisenberg's 1925 paper and there is one point that I feel is crucial yet not explained well enough. After he establishes $x(t)$ as a matrix, calculates $x(t)^{2}$, and talks about non-...
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1answer
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Can one quantize systems with local (non-gauge!) symmetries?

Is it inherently problematic to quantize classical theories with local symmetries? For example, consider the action of EM but now interpret $A_\mu$ as physical. At a classical level, there is nothing ...
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1answer
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(Anti)commutation of ghosts and fermions

I would like to ask whether fermionic Grassmann fields in a gauge theory path integral (say in QCD) should be chosen to commute or anticommute with ghost and anti-ghost fields. The way most textbooks ...
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Gupta-Bleuler and Lorenz Gauge: I don't understand the principle behind Gupta-Bleuler

I would like to make the link between the Gupta-Bleuler Lagrangian and the Lorenz Gauge for Electromagnetism because everything is not clear to me. I am looking for a simple explanation without too ...
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What is “quantization”? Give one example [duplicate]

I just want to know the definition/explanation of quantization in layman's terms. Also an example would be very helpful if provided (not necessary).
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Is it possible to combine two photons of different energies to get a single photon of a higher (combined) energy?

The question itself is pretty self explanatory. I asked this to my chemistry teacher when he was doing the photoelectric effect while teaching atomic structure, and he just shrugged it off. One ...
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Number of photons required for communication

On one hand, the amount of information I can transmit is proportional to the bandwidth. The higher the frequency, the more information I can transmit. On the other hand, the number of photons is ...
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Harmonic Oscillator from a second order Lagrangian: applications

The classical harmonic oscillator is commonly obtained from the canonical first order Lagrangian: $$L_1=\textstyle\frac{1}{2}m\dot{q}^2-\textstyle\frac{1}{2}kq^2$$ However, if you add the term (I do ...
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Physically distinct quantizations

In J. Phys. A: Math. Gen. 22 (1989) 811-822, Crehan considered the classical Hamiltonian, \begin{align} H=\frac{p^2}{2}+\frac{q^2}{2}+\lambda(p^2+q^2)^3\,. \end{align} Due to the presence of the ...
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Keller's correction to the quantization condition: Calculation of Maslov index

I've skimmed over Keller's paper (1958) but I'm still not sure how to calculate the Maslov index for a given Hamiltonian. The quantization condition is given by $$ \int p\,dq = h(n + \frac{m}{4}) $$ ...
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What are the minimal postulates to do quantum mechanics in path-integral formulation without knowing the operator formulation?

I ask this question because many of the books I'm familiar with assumes a familiarity with the operator formulation and then develops the path-integral formulation partly based on a mixture of ...
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Feynman's attempt at QFT theory of graviton as spin-2 particle

Feynman has tried to describe gravitation in term of spin-2 quantum field theory. A quite detailed account is given of this attempt in his "Lectures on Gravitation". However, my grasp of QFT is not ...
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Derivative interaction: $\mathcal{H}_\mathrm{int}\neq - \mathcal{L}_\mathrm{int}$. Question about Feynman Rules

As we known, if there is time derivative interaction in $\mathcal L_\mathrm{int}$, then $\mathcal{H}_\mathrm{int}\neq -\mathcal{L}_\mathrm{int}$. For example, Scalar QED, $$ \begin{aligned} \mathcal{...
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Quantizing one real fermion

It is well-known how to canonically quantize the Lagrangian $L = i \bar{\psi} \dot{\psi} - \omega \bar\psi \psi$ I now wonder how one quantizes the Lagrangian with one real fermion $L = i \psi \dot\...
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Alternative quantization of quantum electrodynamics?

A Quantum field theory is determined, if a Hilbert space Basis with Operators acting on it (such that one element of an Hilbert space is also an element of the same Hilbert space if an Operator acting ...
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First quantization vs second quantization

What is the difference between first quantization and second quantization and where does the name second quantization come from?
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Is the process of quantization a total postulate?

In QFT, we transform a classical lagrangian into a quantum one by transforming our scalar fields into quantum operators. To do so we chose an ordering (Weyl or normal ordering for example), and we ...
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Weyl and Normal ordering in QFT

In my QFT course, if I understood well, we define the normal ordering as the way to quantize a system where we put the creation operators at the left and the annihilation ones at the right. For ...
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Why there is no unique “recipe” for quantization of a classical theory?

I have seen in Wikipedia that different quantization methods exist (see Wiki article with name "Quantization"). Moreover, Wikipedia stated that there is more than one way to quantize a classical ...
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Deriving quantum mechanics from classical mechanics

why most quantum mechanics tools are derived from classical mechanics ? (and everything is ok) why we can do a safe jump from classical scalar quantities (Hamiltonian, momentum, angular momentum, ...
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What does it mean by quantization on phase space?

Quantum mechanical particle's wavefunction are always described by position or momentum representation. Then, I found the so-called quantization on phase space. So, what does it really mean? Does it ...