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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 [discrete] tag instead.

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Canonical commutation relations of quantum fields in null coordinates

To quantize a scalar field, we impose the equal time commutation relations $$ [\Phi(t,\mathbf{x}),\partial_t\Phi(t,\mathbf{x}')] = i\hbar\delta^{(3)}(\mathbf{x-x'}). $$ This can also be generalized to ...
Ratul Thakur's user avatar
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1 answer
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Is it possible to derive Schrödinger's equation from Hamilton's equations?

Accepting the postulates of quantum mechanics, so promoting the classical dynamical variables to operators with appropriate commutation relations, is it possible to "derive" Schrödinger's ...
Noumeno's user avatar
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Possible ambiguities of quantization

Quantization means to replace $p$ (the momentum) in the expressions of classical physical quantities with $-i\hbar\nabla$, so we get an operator belonging to each physical quantity. However, an ...
mma's user avatar
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Anyons and Elementary particles in 2D [closed]

I'm doing my master's degree and I'm starting to learn more about Anyons. I want to understand more deeply why they can exist and how. I've done some research on the internet and found this question ...
Lucas Sievers's user avatar
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Is there a probability distribution associated with fermionic Gaussian states

I am writing this as a mathematician trying to understand fermionic Gaussian states. Up to global phase, a quantum state can be faithfully represented in terms of a quasi-probability distribution on ...
Cole Comfort's user avatar
1 vote
2 answers
115 views

What do we learn from quantizing the relativistic point particle?

In many textbooks on string theory, some time is spend on quantizing the relativistic point particle as a warming-up for quantizing the Nambu-Goto action for relativistic strings. However, I have not ...
Fraxinian's user avatar
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3 answers
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Damped Quantum Harmonic Oscillator with sinusoidal driving force

The standard Damped one-dimensional Harmonic Oscillator with sinusoidal driving force has equation $$\frac{d^2}{dt^2}x(t)+2\zeta\omega_0\frac{d}{dt}x(t)+\omega_0^2x(t)=\frac{1}{m}F_0\sin(\omega t).$$ ...
Riemann's user avatar
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What is the current status (December 2023) of the quantization of Einstein-Cartan Theory?

Einstein-Cartan theory at a classical level is able to "smooth out" some of the singularities in general relativity. Since the presence of singularities is one of the most vexing parts of ...
Panopticon's user avatar
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Equivalence of Quantum Mechanical Systems in Cartesian and Polar Coordinates for a Free Particle [duplicate]

I am exploring the quantum mechanical description of a free particle in 2 dimensions and seeking clarification on the equivalence of formulations in Cartesian and polar coordinates. The core of my ...
A. J. Pan-Collantes's user avatar
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1 answer
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If voltage of x-rays is doubled then intensity of X-rays will be?

My text book says it will remain unchanged because intensity of x-rays depends upon the current and number of electron. If this is true we can also say, the current depends upon voltage. So, why we ...
Amrit Pant's user avatar
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What goes wrong when we quantise a classical system without using $[X,P]=i\hbar$?

Let's say we have a classical system with a Poisson bracket. We quantise this system to get a quantum theory where we choose some variable to operator replacement : $x\rightarrow X, p\rightarrow P$, ...
Ryder Rude's user avatar
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Quantization of electrodynamics in a nonlinear dielectric medium

Recently I read this paper https://doi.org/10.1103/PhysRevA.30.1860 by Hillery and Mlodinow about the (canonical) quantization of electrodynamics in nonlinear dielectric media. They assume that the ...
WillHallas's user avatar
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Canonical quantization of gauge field under the Schwarzschild background

I have read some papers (e.g.0803.2001, PhysRevD.24.297, especially section 4 in 1809.03467 ) to find the mode expansion of gauge field under the Schwarzschild background. In paper PhysRevD.24.297, ...
Lain's user avatar
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2 answers
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Why can't we "simply" quantize Maxwell's equations without a Lagrangian to create a quantum theory of electrodynamics?

Useful quantum field theories like quantum electrodynamics (QED) suffer from a litany of problems related to the fact that, at least in their usual Lagrangian formulation, interactions between the ...
The_Sympathizer's user avatar
5 votes
2 answers
281 views

Dirac procedure for Wheeler De Witt equation

After computing the Hamiltonian constraint and the momentum constraint in general relativity the Hamiltonian constraint is turned into an operator equation and solved in a manner similar to a ...
Dr. user44690's user avatar
3 votes
1 answer
101 views

Asking for explanation of Einstein's critique of the non-invariance of Bohr-Sommerfeld quantization

I am looking to understand better what problem might come from the claimed non-invariance of the Bohr-Sommerfeld quantization, which Einstein criticizes in his article On the Quantum Theorem of ...
Epsilon Away's user avatar
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Does geometric quantization work for second quantization?

I have been studying geometric quantization, and was wondering if a similar method could be employed for the second quantization. I imagine such a setup would involve “going up a level;” our “phase ...
moboDawn_φ's user avatar
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1 answer
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Naive first-quantization of the Dirac field?

To begin with, please note that I am fully aware of the differences between the confusingly named "first quantization" and "second quantization", and how they correspond to ...
Lateralus's user avatar
3 votes
1 answer
192 views

Loop Quantum Gravity vs Polymer Quantization

What is the linkage between Loop Quantum Gravity and the approach of the Polymer Quantization? I know you get a lattice using the correct polymer representation, so that's a good toy model for the ...
LolloBoldo's user avatar
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Deriving the ghost Lagrangian in Peskin and Schroeder

On page 514 of Peskin and Schroeder, the book derives $$\tag{16.31} \det\bigg(\frac{1}{g}\partial^\mu D_\mu\bigg)=\int\mathcal{D}c\mathcal{D}\overline{c}\exp\bigg[i\int d^4x\overline{c}(-\partial^\mu ...
Simplyorange's user avatar
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1 answer
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Classical systems with compact phase space

In the Hamiltonian formalism of classical mechanics, a system with configuration space $Q$ is represented by a symplectic manifold $(T^*Q,\omega^\mathrm{can})$ called the phase space. The dynamics are ...
Fraxinian's user avatar
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Can we call it "quantization" when we specify Hilbert space and operators to write a classical field theory into a quantum theory?

Can we call it quantization when we specify Hilbert space and operators to write a classical field theory into a quantum theory? Suppose there is a single spin 1/2 system with Hamiltonian $\hat{H}=\...
Zuo's user avatar
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3 votes
0 answers
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Integration measure for Polyakov's path integral

In section 3.4 of Blumenhagen's Basic Concepts in String Theory, where path integral quatization is presented, and we are given the partition function for the Polyakov's path integral $$Z=\int \...
Sofvar's user avatar
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7 votes
2 answers
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Is Loop quantum gravity an unadulterated quantisation of general relativity, or does it have additional assumptions?

I was reading this Phys.SE answer written by user346. At the end of point 3, they say they've only made a change of canonical variables from the ADM formalism to get the Ashtekar formalism. Then point ...
Ryder Rude's user avatar
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2 votes
1 answer
183 views

Using the EoM in the canonical quantization of EM field

Starting from the classical electromagnetic field, there two approaches to quantization that I want to compare. The problem arises when I write the classical fields in terms of $a$ and $a^*$, which ...
Mr. Feynman's user avatar
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4 votes
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Why is the vibration of chemical bonds quantized but the rotation about single bonds in molecules is not? [closed]

Vibration of bonds molecules is quantized. Rotation of entire molecules is quantized. Rotation about single bonds in molecules is not quantized.
Darrell J. Woodman's user avatar
6 votes
2 answers
250 views

"Constrain then quantise" vs. "quantise then constrain"

Consider a classical system whose configuration space is a manifold $M$, and which is subject to some constraint $\mathcal{C}=0$. [E.g. the system could be a particle moving in $M=\mathbb{R}^n$, with $...
nodumbquestions's user avatar
5 votes
1 answer
213 views

Does geometric quantization work for arbitrary "particle with constraint + potential" systems?

I was struck by the following line in Hall's Quantum Theory for Mathematicians (Ch. 23, p. 484): In the case $N = T^*M$, for example, with the natural “vertical” polarization, geometric quantization ...
WillG's user avatar
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1 vote
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When are two quantum descriptions / models equivalent?

I am occupied with different types of quantization methods for constrained systems. I start with a constrained phase space and then follow two different paths to get rid of the constraints. In the end,...
Viktor Zelezny's user avatar
1 vote
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Does $H=V(p) +x^2$ give a well-behaved Quantum Theory?

$V(p) $ is the Coulomb potential. I think this theory should be fine because Hamilton's equations are somewhat symmetric in $x$ and $p$. The momentum space Schrodinger equation will be: $$i\frac{d\psi ...
Ryder Rude's user avatar
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3 votes
0 answers
114 views

Is there a both manifestly covariant and unitary formalism of Quantum Field Theory?

The Lagrangian formalism is only manifestly covariant and the Hamiltonian formalism is only manifestly unitary. In classical field theory, there exists the De Donder Weyl formalism, which is ...
Ryder Rude's user avatar
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2 votes
1 answer
174 views

Light-cone quantization of open string as derived in Polchinski

Polchinski uses the following gauge conditions, but I don't follow this procedure of gauge fixing and quantization: \begin{align} X^+ = \tau, \tag{1.3.8a} \\ \partial_\sigma \gamma_{\sigma \sigma} = 0,...
physicsbootcamp's user avatar
3 votes
2 answers
203 views

What if we skip polarization in geometric quantization?

In QM, we most frequently work with "position-space" representation of the CCR $$ \mathcal{H} = L_2(\mathbb{R}, dx), \quad X = x, \quad P = - i \hbar \frac{d}{dx}. $$ Sometimes it's useful ...
Prof. Legolasov's user avatar
3 votes
1 answer
177 views

Constructing a field theory action for the point particle in curved space

The point particle action in the Hamiltonian formalism is $$ S = \int d\tau \Big( -p_\mu \dot{x}^\mu - \frac{e}{2}(g^{\mu\nu} p_\mu p_\nu - m^2) \Big) \ ,\tag{1} $$ where I explicitly displayed the ...
myorbs's user avatar
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2 votes
1 answer
62 views

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 ...
tgsweat's user avatar
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1 vote
0 answers
26 views

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{...
Adrien Amour's user avatar
1 vote
0 answers
55 views

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 ...
dennis's user avatar
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2 votes
2 answers
235 views

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 ...
Gere's user avatar
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1 vote
0 answers
91 views

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 ...
Joshua G-F's user avatar
6 votes
1 answer
322 views

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 ...
Simplyorange's user avatar
1 vote
1 answer
200 views

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 ...
leob's user avatar
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1 vote
0 answers
40 views

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 ...
GedankenExperimentalist's user avatar
0 votes
0 answers
43 views

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 ...
More Anonymous's user avatar
1 vote
1 answer
121 views

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 ...
xpsf's user avatar
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1 vote
2 answers
216 views

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 ...
M.N.Raia's user avatar
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2 votes
1 answer
203 views

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. ...
chaveroche's user avatar
3 votes
2 answers
170 views

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 ...
Noumeno's user avatar
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0 votes
2 answers
168 views

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 ...
BarrierRemoval's user avatar
1 vote
0 answers
48 views

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 ...
Nathanael Noir's user avatar
5 votes
2 answers
352 views

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 $$ \...
DeafIdiotGod's user avatar

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