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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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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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1answer
133 views

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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36 views

Quantization on (2,1)-signature hyperplane

QFT states, roughly speaking, belong to a certain subset of functionals over the field configuration on the space-like hyperplane, usually chosen as $t = 0$. What would happen if we chose a mixed-...
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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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2answers
58 views

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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38 views

Quantizing the double pendulum hamiltonian

So, just for kicks, I thought it might be fun to try to see what happens if you have a "quantum double pendulum". Take a simple point pendulum with mass $m$ and length $l$, and hang a second identical ...
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1answer
112 views

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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1answer
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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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64 views

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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0answers
47 views

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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1answer
110 views

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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1answer
36 views

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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1answer
87 views

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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2answers
103 views

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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0answers
42 views

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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1answer
98 views

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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1answer
143 views

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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1answer
48 views

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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1answer
55 views

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
60 views

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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108 views

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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1answer
58 views

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
151 views

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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0answers
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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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2answers
245 views

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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106 views

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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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
174 views

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
392 views

(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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1answer
829 views

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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3answers
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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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1answer
795 views

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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1answer
178 views

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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230 views

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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1answer
250 views

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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1answer
351 views

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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575 views

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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1answer
160 views

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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1answer
172 views

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?