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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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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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,...
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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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Why secondary constraints in Quantum Theory?

I am self-studying dynamics of constrained systems and their quantisation from Rothe and Rothe book "classical and quantum dynamics of constrained systems". While using Dirac quantisation, ...
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How can a classical phase space be unquantizable?

On page 2 of the paper "2 + 1 dimensional gravity as an exactly soluble system" Witten claims that: Depending on its topology, a finite-dimensional phase space might be unquantizable, How ...
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Can one quantize Chern-Simons theory in the covariant phase space formalism?

The covariant phase space, which coincides with the space of solutions to the equations of motion, gives a notion of phase space which does not rely on a decomposition of spacetime of the form $M=\...
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Is it possible to minimize the number of axioms/rules of the canonical quantization?

In the standard canonical quantization procedure there are two rules. Transform all quantities to operators. Transform the Poisson bracket to a commutator. Of course it will be nicer to minimize the ...
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Polarization procedure in geometric quantization

The geometric quantization can be considered as an approach the formalize the way of associating a quantum theory corresponding to a given classical theory. Suppose we start with a sympetic manifold $(...
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Quantization and Commutation Relations

Why do we use commutation relations when quantizing any system? In the case of developing quantum mechanics from classical mechanics, we write the hamiltonian and then quantize it by having the ...
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WHY BRST formulation works: Conditions imposed on QFT to find (how many) BRST parameters

question: WHY BRST formulation works? In more details: What are the conditions we need to impose on QFT to find the BRST (global) symmetry? Why can we demand the BRST parameter $\epsilon$ directly ...
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Use the commutation relation to show that the conjugate momentum acts on eigenstates of $\hat{\Phi}$ as $ - i \delta / \delta\phi_a(\mathbf{x})$

This is part (b) of Schwartz's Problem 14.3 in his Quantum Field Theory and the Standard Model textbook. Suppose that we have a real scalar field operator $\hat{\Phi}(x^0,\mathbf{x})$ with conjugate ...
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Why is radial ordering necessary?

Suppose I have some conserved charge in a 2 dimensional CFT $$Q(|z|)=\int_{w=|z|}\text{d}w\,T(w).\tag{1}$$ The infinitesimal transformation induced on a field $\phi$ at $z$ is then $$[Q(|z|),\phi(z)]=\...
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What is the "secret " behind canonical quantization?

The way (and perhaps most students around the world) I was taught QM is very weird. There is no intuitive explanations or understanding. Instead we were given a recipe on how to quantize a classical ...
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Operator traces in Kontsevich quantization

In quantization, one studies maps from functions on the phase space to operators acting on the Hilbert space. Let's fix one such map and call it $Q$. Deformation quantization is based on the idea that ...
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