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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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131 views

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 ...
29 views

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 ...
75 views

162 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 ...
37 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-...
42 views

71 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 ...
58 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 $p$...
123 views

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....
120 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 ...
55 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 $\lbrace f, \gamma\rbrace \neq 0$...
82 views

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 ...
92 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 $S$...
111 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 ...
81 views

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 ...
104 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,...
151 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 ...
52 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 ...
403 views

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 ...
62 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 ...
69 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 ...
111 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 ...
77 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 ...
59 views

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 ...
189 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 ...
68 views

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 ...
277 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 $\mathcal{M}$ ...
115 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 ...
6k views

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?...
252 views

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 ...
142 views

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-...
200 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 ...
414 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 ...
990 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 ...
4k views

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).
958 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 ...
194 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 ...
292 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 ...
277 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 ...
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 $$\int p\,dq = h(n + \frac{m}{4})$$ ...