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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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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Center symmetry on wavefunction

Assume we know the wavefunctions of a SU(N) Chern-Simons (or YM) on a 3-mfld $M$, perhaps using holomorphic quantization. How do the center symmetry transformations act on the wavefunctions? Is it ...
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Is this four-step recipe for quantization always valid?

I know that there is more than one way to go about quantization, but operationally, I find it useful to have a go-to set of steps that can convert a classical system to its quantum analog. Is there ...
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Quantization of an $\mathcal{c}$-algebra

I don't know if this is a valid question to ask, but I am wondering about the following: We are given a set of $\mathcal{c}$-number Lie-Brackets $$ [q_i,q_j] = 0= [p_i,p_j] \\ [q_i,p_j] = c_{ij}, $$ ...
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Quantization of $c$-number Dirac-Bracket

I have a question concerning the quantization of phase-space variables $(q_1, q_2, q_3, p_1, p_2, p_3)$ with the Hamiltonian $$ H = \frac{3}{2}(p_1^2+p_2^2 +p_3^2) $$ and the following non-commuting ...
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Do we understand why mass, charge or magnetic moment appear as quantized quantities?

There are two similar questions as the comment notified: 1. Reason for the discreteness arising in quantum mechanics? 2. How does quantization arise in quantum mechanics? I could see two points there: ...
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Validity of Canonical Quantization

I was studying about what does it mean canonical quantization treatment. But now I have the next question. Why if we establish canonical the commutation relations $$\left[q,p\right]=i\hbar,\quad \left[...
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Batalin-Vilkovisky quantization

Batalin-Vilkovisky (BV) quantization is way of quantizing a theory, which is apparently more powerful than BRST quantization. It has been used, for example, for string field theory, in the closed ...
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Fock Space representation for 1D Square Well Potential

I will make a few observations (if any of these is incorrect please let me know) and then ask my question :- i) For a Quantum Mechanical Harmonic Oscillator (QMHO) we have, at least, two kinds of ...
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Experimental verification of quantization

I understand quantization as a map from Symplectic Manifolds $M$ (either finite dimensional or not) to Hilbert Spaces $H$, along with a rule that attach to every function $F$ in $M$ a hermitian ...
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Gauge Symmetries as Redundancies vs Constraints

I am very confused by these two points of view. Consider a theory whose space of fields is $V$ and that has an action $S$. Thinking of a gauge symmetry as a redundancy is your description means that ...
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Why does a square root term make the quantisation of action difficult?

When going over my lecturer's notes on String Theory and trying to understand a particle as a theory of gravity in 1D, it is mentioned that the action $(1)$ is regularisation invariant, $$S=-m\...
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Name of concept: Replace classical variables by quantum operators

I feel like there was a name for this sleight of hand approach and I've been unsuccessfully trying to google it for a while. I think Heisenberg introduced it and it's basically "putting hats on ...
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Non-relativisitc Quantization of Classical Fields

When quantizing a theory of one particle, we are used to taking the classical dynamical variable $\gamma:\mathrm{time}\to\mathrm{space}$, the trajectory in time, and replacing it with another, ...
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On quantization of relativistic quantum theory on curved space

In his book "Lectures on quantum mechanics", at the end of chapter 3, Dirac states that "it does not seem possible to fulfill the conditions which are necessary for building up a relativistic ...
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How do the electrons absorb energy in an discharge tube that is used for produce an emission spectrum?

When there's hydrogen in a discharged tube it produces an emission spectrum, emitting energy(photons). (Eg:-When an electron jumps from 3rd energy level to 1st energy level, the electron emits a ...
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Experimental tests of operator ordering

In quantization, we frequently run into ordering ambiguities. In general, this means that there can be inequivalent quantum theories corresponding to the same classical theory. Has there ever been an ...
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What do we mean by radial quantisation in CFT?

When we quantise QFT we do that in equal time slices. In CFT it is useful to use equal radius slices. Why is that the case? And what does it mean?
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General question about quantization procedure

As far as I understood, when we want to quantize a system, the procedure can be the following (but probably not the most general one): We start by writing down the Lagrangian of the system. We ...
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Planck's Hypothesis Derivation

Max Planck in 1900 used the quantisation of energy to explain black body radiation. Using what principles did he arrive at his final formula $E=nhv$?
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Why various molecules in an ideal gas at a particular temperature can have only quantized energies?

Why various molecules in an ideal gas at a particular temperature can have only quantized energies? Why can't they have the energies distributed in a continuous fashion? Following is an image taken ...
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Canonical Quantization: Hamiltonian limitations

Before performing a canonical quantization there are some features of the Hamiltonian that have to be taken into account. For example, the hamiltonian has to be symmetric in order to be self-adjoint. ...
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Quantising Classical Lagrangian

Suppose you have a system described by the following Lagrangian: $$L=(1-gq²)\dot{q}^2/2.$$ How would you quantize this theory? Do you need to symmetrize the Hamiltonian before promoting the ...
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Quantization of the Nambu bracket

The most simple quantum mechanical system consists of a canonical pair of operators $\{P, Q\}$ satisfying $$ P Q - Q P = i \hbar. $$ It is well known that there is a unique (modulo unitary maps) ...
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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 ...
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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 ...
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What's the difference between canonical quantization and second quantization?

I am wondering the difference between the canonical quantization and the second quantization in quantum field theory. For example, a harmonic chain, one can write down its lagrangian density $\...
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Single electron in conductive cavity

It is a basic result in electrostatics that a charge $q$ in an arbitrary cavity of an ideal conductor will generate a total charge $-q$ on the surface of the cavity in such a way that the electric ...
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Obstruction in quantization. Weyl Ordering

What is an obstruction in quantization? I've found that obstructions object of the study of a mathematical theory, previously concerned with homotopy. The problem is that to explain what an ...
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Creation and Annnihilator Operators: generality and meaning

I am studying my fisrst course in quantum mechanichs where we treated the example of the Harmonic Oscillator through the Weyl Heisenberg Spectrum Generating Algebra Method. In that context we ...
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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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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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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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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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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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