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 [discrete] tag instead.

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De Broglie's hypothesis for and resulting reasons for the lack of absorption of photons not at the specific discrete energy levels required

Essentially what the title is. Although I know de Broglie's standing wave model for electron orbits has problems, I have a question regarding why atoms will not absorb photons not of the specific ...
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Is the expectation value of an operator obtained by canonical quantisation always the classical value? [closed]

I understand that generally, for some Hermitian operator $\hat{A}$, the classically measured value of a system is given by \begin{align} \langle \hat{A}\rangle=\langle\psi| \hat{A}|\psi\rangle \end{...
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Mode expansion for $p$-branes

In the quantization of $p$-branes, for $p>1$ what is the mode expansion? What I am after, more specifically, is: what is the configuration around which the expansion is made? For example, for the ...
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Why does the Dirac Lagrangian not already use operators (instead of canonical quantization)?

I've learned that in canonical quantization you take a Lagrangian, transform to a Hamiltonian and then "put the hat on" the fields (make them an operator). Then you can derive the equations ...
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Derivation of Equation 10.97 in Zettili: Quantization of the EM Field

I am reading through Zettili, and I am stuck on one of the steps that Zetilli makes when quantizing the EM field, specifically with page 567. Zettili first introduces the Fourier series for the ...
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Path integral quantization of the EM field in Peskin and schroeder

I'm studying path integral quantization of the electromagnetic field using Peskin and Schroeder secdtion 9.4. We want to compute the functional integral $$\tag{9.50} \int \mathcal{D}A\,e^{iS[A]}.$$ We ...
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Operator Ordering Conventions and Symmetry

Quantization procedures may need operator ordering conventions to avoid ambiguity. In classical theories, classical observables are often described by smooth functions, so the order of observable ...
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Mathematical equivalent of Fundamental nature of charge [closed]

How to mathematically represent the fact that electric charge is a fundamental quantity? i.e. that it cannot be explained in terms of other things, for example, the normal force can be explained as ...
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The equivalence principle and the existence first quantization?

So imagine we are doing Einstein's famous thought experiment where we are locked in an elevator so narrow we are unable to detect tidal forces. The equivalence principle suggests that we should be ...
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First and second quantization of relativistic mechanics

Classical mechanics can be written in a lagrangian formalism. If one quantizes this theory, we get quantum mechanics. Let us continue this process: Relativistic mechanics can also be written in a ...
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Doubt on the geometry of "quantum phase space"

In Jose & Saletan's "Classical Dynamics", they show the global structure of Hamiltonian mechanics: you then have a $Q$ manifold (configuration space), and the phase space structure is ...
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Wave equation for lightcone coordinate $X^-$

A quick question from Polchinski volume.1 : He claims in p.20 that the worldsheet lightcone coordinates $X^\pm$ also (i.e. in addition to the transverse coordinates $X^i$) satisfy the wave-equation. ...
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What does it mean to "quantise" a system?

Suppose we have a physical system, let's say a ring of $N$ atoms held together by elastic force. (This is just an example, we could have picked any physical system) Classically we can easily find the ...
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Are there quantum gravity theories in which spacetime itself is regarded as quantum in nature?

In quantum gravity, it's tried to quantize the gravitation. However, if I got it correctly, most quantum gravity approaches try only to quantize gravity as a force, the curvature of spacetime, not the ...
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Confusion about the definition of negative angles between two D-branes

I have a conceptual question regarding a paper I am reading. More precisely, the first appendix starting on page 29. In this paper, schematically, the classical oriented open strings get quantised ...
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What physical observables are the creation/annihilation operators for the EM field made from?

The explanations of quantizing the Electric/Magnetic (E/M) fields that I've read have all basically worked by using the Coulomb gauge in free space to define the vector potential in some volume as $$ \...
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Basic question in similarities and difference on quantizations

In physics, usually quantization means canonical quantization. i.e., which we treat classical objects to quantum operators. i.e., For the association $Q:f \mapsto \hat{f}$ from functions on the ...
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Momentum operator in Geometric Quantization vs momentum operator on arbitrary curved space(time)s

In the following stack exchange post Momentum Operator in curved spacetime (QFT) a general expression for the momentum operator is given for a Riemannian manifold $(M,g)$. Similarly, Frederic Schuller'...
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Physical motivation of quantization

I am a mathematics student recently looking into (geometric and deformation) quantization. I'd like to know more about their physical motivations. Here by "quantization" I mean any process ...
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About Loop Quantum Gravity and concerns with its "polymer" quantization. Has it ever been addressed or answered/justified?

Referring to Why is Standard Model + Loop Quantum Gravity usually not listed as a theory of everything Underlying papers are: J. W. Barrett, “Holonomy and path structures in general relativity and ...
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The different frameworks around the string

I am studying string theory and I realize that the relations between the different frameworks are not clear to me. Following this question, one could repeat the discussion but now taking $p=1$. We get ...
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The different frameworks around the point particle

I am studying string theory and I realize that the relations between the different frameworks are not clear to me. Starting from (reativistic) classical mechanics, the "state" of a point ...
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Quantum field theory not related to classical field theory [duplicate]

Overvation 1: Whatever quantization process is used, it is common to define a QFT from a classical field theory. Observation 2: On the other hand, given a lagrangian QFT, one could try to "...
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Geometric Quantization of Dirac spinor in QFT

I have been using resources such as, Geometric quantization, Baykara Uchicago, to get a deeper insight into geometric quantization. However, it seems to me that this theory is only valid for quantum ...
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Order of product of $x$ and $p$ while deriving Hamiltonian from a Lagrangian in Quantum Mechanics

Everyone who has taken a course in Quantum Mechanics has at some point derived a quantum Hamiltonian from a Lagrangian. However, I can't seem to find any reference on the topic. My question is ...
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Does it make sense to quantize perfect fluid?

Wikipedia (see here) says perfect fluid may be quantized. I do find an article (arXiv 1011.6396) about this, and the procedure is straight forward. What I do not understand is whether this ...
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Discrepancy between the two different equations of the momentum operator

i am doing a thesis on the quantization of a real scalar field in a gravitational wave background. I am doing this in lightcone coordinates, so $u$ is $z-t$. I start with an action and define a ...
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When can we quantize the Hamiltonian for an LC circuit?

For a superconducting qubit, we start with an LC circuit and "quantize" it, mapping the variables analogously to the variables for the harmonic oscillator. In general, when are we allowed to ...
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1 answer
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A Hamiltonian with a potential depending on the momentum

Imagine we have a Hamiltonian, whose potential depends on velocities (and hence on the momentum), like, for example, $$ H= \frac{p^{2}}{2m}+ V(x,p)$$ then how can I quantize that?
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Function of noncommutative operators: how should the powers in its Taylor expansion be arranged, and how to take partial derivatives?

Let $F:\mathbb R ^n\to\mathbb R$ be a function that has a Taylor expansion, then it can be written (expanded at $a$) as $$ F(x)=\sum_{\alpha} \frac{(x_1 - a_1)^{\alpha_1}\dots(x_n - a_n)^{\alpha_n}}{\...
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Quantization of the Gibbs distribution

Consider a simple quantum mechanical system, for example, the 1d harmonic oscillator. Given the inverse temperature $\beta$, the classical Gibbs distribution is the following function over the phase ...
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Quantum corrections in the phase space formulation

I'm trying to reconcile the following two statements: Quantum Mechanics gives physical predictions which are different than the predictions that are obtained in the $\hbar \rightarrow 0$ limit, that ...
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Planck-scale curvature in covariant LQG and quantization of length: does LQG apply also to the Planck-regime?

In the covariant approach of loop quantum gravity (see http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf ), the theory is defined on a "lattice", similar to lattice QCD. In this case ...
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Question about canonical quantization of the open string ghost system

In section 3.1.3 of Green, Schwarz and Witten book on superstrings, it is stated that the canonical anti commutation relations for the fermionic ghosts are $$ \{ b_{++}(\sigma, \tau), c^+(\sigma', \...
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Photon emmision from an accelerating particle

How does an accelerating charged particle emit a quantized photon? Quantization of light makes sense to me if we were talking about vibrating charged particles or electron orbitals. But what about a ...
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Is the "Push-Down" Quantization of Chern-Simons Theory part of a more general approach to Quantization?

I've recently started reading Axelrod, Della Pietra and Witten's original paper about the quantization of Chern-Simons theory. I'd like to know if the "push-down" quantization strategy they ...
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$\hat q \hat p$-quantization

I'm looking through the Berezin's paper 1971. And there are a couple of question that confuse me. It's clear why we need to use quantization procedure, because of the uncertainty principle and ...
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Hamilton's equation for generating functional

I've been reading E. S. Fradkin and G. A. Vilkovisky, “Quantization of Relativistic Systems with Constraints: Equivalence of Canonical and Covariant Formalisms in Quantum Theory of Gravitational Field....
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Discretized conserved values without necessarily using gauge symmetries

All of the examples I have seen for discrete conserved values (e.g. charge) invoke gauge symmetries, and thus extra degrees of freedom. Is it possible to have a discretized/quantized conserved values ...
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What is the third quantization and the creation and annihilation operators of universes?

We have only recently begun to undergo secondary quantization, and I know that for the introduction of the creation and annihilation operators, the existence of interacting quantum fields is necessary,...
2 votes
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How to quantize a system if kinetic energy depends on coordinate?

In a standard physics course we usually learn that quantization of a system is ambiguous if momentum and position happen to be multiplied in the classical Hamiltonian (i.e. the classical Hamiltonian ...
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Why are commutators the first choice in describing observables that cannot be measured simultaneously?

In quantum mechanics, we convert Poisson brackets to commutators for the observables to account for the uncertainty principle. However, I do not understand why do we do this. What motivates us to ...
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Quantization of electromagnetic field: from free-space to media

When studying the quantization of the electromagnetic field, one seems to always derive everything for free space (no charges/currents). This involves solving Maxwell's equations to find modes (in ...
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Why are first class constraints harder to quantize than second class constraints?

I understand that the well known system with the second class constraints: \begin{align} &q_1 = 0 \\ &p_1 = 0 \end{align} has the apparent problem when performing quantization using the ...
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When a long wave photon is emitted by an electron, how come it is perfectly symetrical?

A long-wavelength, e.g. radio frequencies, of say, 1 km, has a period lasting about 1/300000th of a second. So for an imaginary fixed observer watching the incoming wave, it takes some time to go from ...
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Global mathematical structure of QFT

"Classical" gauge theories (e.g. electrodynamics combined with quantum mechanics) have the following global description: $A_{\mu}$ is a connection in a principle bundle The matter fields ...
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Some elementary relations in the quantization of a compact smooth symplectic manifold [closed]

In section 6.1 of https://arxiv.org/abs/1903.10792v1, there is a summary of relations in quantization on a compact symplectic manifold. These relations are as follows: $(M,\omega)$ compact $C^\infty$ ...
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Failure of canonical quantization of holonomic constraints

I am curious to know why canonical quantization fails for systems with holonomic constraints (dependent only on the position canonical variable). When googling, I notice that there is a lot of ...
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What is the rigorous definition of the verb "to quantize"?

I've studied QM and QFT for a couple of years now, so I'm familiar with the tersm "quantize", "quantization" and so on. I'm obviously also familiar with the Lagrangian description ...
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Difference between field-antifield and light-cone quantisation

I have learnt field-antifield quantisation and know that it can be used for very general gauge theories - open and reducible. I have not got much into light-cone quantisation but I am unable to see ...

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