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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flux quantization in superconducting ring

I am trying to understand SQUID microscopy from the ground up, so I am starting with flux quantization in superconducting rings. I found a nice presentation that covers some of the details, but I am ...
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Quantizing highly nonlinear field-theories?

I'm wondering how to go about quantizing a classical field theory which looks nothing like a free field theory plus a perturbation term. Suppose for concreteness I have the classical hamiltonian $ ...
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Weyl Ordering Rule

While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian ...
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In the Holometer experiment, why would one of the split laser beams arriving back at a slightly different time indicate the universe was quantized?

All the pop-sci articles I've read have a description of the set-up similar to this: It uses a pair of laser interferometers placed close to one another, each sending a one-kilowatt beam of light ...
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42 views

Feynman Path Integral as a Quantization Scheme

Why isn't the path integral usually discussed as a quantization scheme, like geometric and deformation quantization? Was searching wikipedia for this.
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124 views

$\pi$, $\sigma$ - atomic transitions with respect to the magnetic field axis

I am confused about the atomic transition with different polarized lights. I post the pictures as follows. There are four cases. In case 1, the right-handed circular polarized light ...
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1answer
56 views

How to impose canonical commutation relations when quantising a field

I believe this is a simple question, however I cannot find it explained anywhere what the term: "Impose canonical commutation relations" means. If I have a classical equation, and I wish to quantise ...
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63 views

Regge trajectory and Kaluza Klein tower

The mass of hadrons in the Regge trajectory scales as $m=\sqrt{\frac{J}{\alpha}-\alpha_0}=\sqrt{\frac{n}{\alpha}-\alpha_0}\propto \sqrt{n}$, where $J=n$ is the spin of the particle (in natural ...
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75 views

Questions about Quantization and Noncommutative Geometry

I am trying to orient myself among the vast amount of literature, trying to study the prerequisites necessary for gauge theory and theoretical physics. I have an undergraduate degree in mathematics ...
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16 views

Why spurious pulses are likely in partial discharges?

My notes The gas multiplication in the proportional counters is based on the secondary ionization created in collisions between electrons and neutral gas molecules, resulting in some visible ...
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3answers
209 views

Difference between discretization and quantization in physics

I am just trying to understand the fundamental difference between these two concepts in physics: From discreteness of some quantity: one usually interprets it as a quantity being only able to take ...
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1answer
201 views

How is quantization related to commutation? [duplicate]

How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence ...
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2answers
79 views

Magnetic Flux Quantization

I remember a few years back in my introductory AC/DC circuits class reading a little bit in the back of the book about magnetism. By this point, I was well aware that magnetic fields are commonly ...
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Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
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Quantizing Klein-Gordon via Lie Groups [closed]

I'm trying to understand second quantization of the Klein-Gordon equation, as explained in, say, standard books like Peskin and Schroder, but using the language of Lie (representation) theory. In a ...
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5answers
764 views

When is energy discrete/quantized for a potential well?

Specifically, my question is: Should one expect energy quantization for a particle in the following potential well? More generally, how can one tell whether or not energy should be ...
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108 views

What new does geometric or deformation quantization give to physics? [closed]

What new does geometric quantization or deformation quantization give to physics? For example: prediction of new physical phenomena or just better tool for quantization. What can these schemes do in ...
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References on deformation quantization

I'm looking for books or introductory review papers or lecture notes on the topic of deformation quantization. (And preferably, geometric quantization as well.) I'm mainly interested in the ...
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359 views

Geometric quantization of identical particles

Background: It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold ...
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3answers
197 views

Semiclassical quantization of bouncing ball

Consider an elastically bouncing ball of mass $m$ and energy $E$. This has a triangular potential $$ V(x)~=~\left\{\begin{array}{ll} mgx & \text{if } x>0, \\ \infty & \text{if } x<0, ...
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92 views

Discontinuity of paths in phase space path integrals

Berezin's famous paper "Feynman path integrals in a phase space" discusses the space of paths on which the phase space path integral is concentrated. In particular, these paths are known to be ...
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56 views

Projection that keeps graviton but gets rid of B-field

We consider the closed superstring and the massless states in the (NS,NS)-sector \begin{equation} \tilde{b}^i_{-\frac{1}{2}} |0\rangle_L \otimes b^j_{-\frac{1}{2}} |0\rangle_R. \end{equation} It is ...
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45 views

The relation between commutation and quanta

This question discusses discretization in some sense, and this question talks about how quantization and Hilbert Spaces are related (the answer seems to to be not at all), but what I'm curious about ...
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2answers
83 views

Why is the introduction of a quantization volume necessary for quantization of the EM field

I have been working through the quantization of the electromagnetic field, and every source I find introduces a quantization volume with periodic boundary conditions in the process, in which we fit ...
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1answer
121 views

Dirac bracket for the Majorana Lagrangian

Note: See update below. Consider the Majorana Lagrangian $$\mathcal{L}=-\psi ^{\mathrm{T}}\mathrm{i}% \gamma ^{0}\left( \gamma ^{\rho }\partial _{\rho }+m\right) \psi ,\tag{1}$$ where $% \psi \in ...
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Analogy between a classical discrete system and non classical continous system

Most introduction textbooks about quantum fieldtheory start with a discrete classical harmonic oscillator and then looks at it in the continuous quantized case (quantized field). This leads to the ...
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1answer
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Canonical commutation relations in Light-cone gauge

It seems that when trying to identify the physical degrees of freedom for the string some authors$^1$ use: $$ q^-=\frac{1}{\ell}\int_0^{\ell} X^-(\tau,\sigma)d\sigma$$ Then, the commutation relation ...
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174 views

How to mathematically describe a spin-0 particle [closed]

I don't know all the technical things like Eigenstates. I want to know, mathematically written out for beginners, how to make a quantum field theory of a scalar boson. To spare confusion- I understand ...
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1answer
139 views

Can I Weyl-order the following Hamiltonian?

I am trying to perform a path integral but I am having trouble with the Weyl ordering of my Hamiltonian. The Lagrangian of the system in question is $$L~=~\frac{1}{2}f(q)\dot{q}^2,$$ where $f(q)$ ...
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1answer
142 views

What is the idea behind canonical quantization?

From what I understand, canonical quantization of a classical theory consists of replacing the observables by abstract operators, of which only the commutation rules, which have to correspond to the ...
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40 views

Why should we want to quantize Gravity? [duplicate]

I understand that it will be "nice" to have a quantum description of Gravity as well, just like the other 3 forces. I would like to find out what problems arise in existing theory (not counting String ...
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1answer
88 views

Under what cases is the Batalin-Vilkovisky (BV) operator nilpotent?

It is understood that when we deal with gauge algebras which close on-shell only after using equations of motion or where the space-time is curved, we can no longer just do away with BRST ...
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67 views

Tropical Geometry and Quantization

Recently I saw this question posted on Math Overflow asking about the motivations behind tropical geometry. The OP mentions that tropical geometry can be viewed as the classical limit of regular ...
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9answers
3k views

Is a “third quantization” possible?

Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
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Quantization of a free field: Klein-Gordon case

I am a beginner and reading this course text on QFT. The author first introduces the KG equation: $$\partial_\mu\partial^{\mu}\phi+m^2\phi=0$$ [with Minkowski signature $(+,-,-,-)$]. Then the ...
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53 views

Volume factor in Faddeev-Popov quantisation

In Faddeev-Popov quantisation, why does the integral over gauge parameter cancel the volume factor of the gauge group that's in the denominator? In fact, I don't understand where the volume factor ...
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1answer
280 views

What is “momentum density” and why it important to QFT?

I am reading Quantum Field Theory for the Gifted Amateur. On page 98, they provide a summary of a basic canonical quantization procedure: Step I: Write down a classical Lagrangian density in ...
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How to associate a Hilbert space with a QM system?

I couldn't really find a fitting title for this question. I'm still relatively new to QM and am trying to get the basics down. I understand that a physical system is associated with a Hilbert Space, ...
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1answer
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Divergence in the total momentum opertator in QFT

The classical expression for the total momentum operator is $$P^{i} = -\int d^3x \, \pi(x) \, \partial_{i} \phi(x),$$ which, after second quantisation, using $$\hat{\phi}(x) = \int \frac{d^3k}{(2 ...
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1answer
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Connections between classical mechanics and quantum mechanics [duplicate]

I've been studying quantum mechanics and classical mechanics for a little while now, and I still don't feel as though I fully understand the motivation for some of our choices in Heisenberg mechanics. ...
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3answers
92 views

Quantization conditions/ Real Scalar field

It is often written in books, the quantization conditions for classical field theory leading to Lagrangian of a real scalar field and thus to Klein Gordon equation. And these are introduced by ...
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2answers
163 views

Dirac bracket and second class constraints in first-order gravity formalism

In the first order formulation of general relativity, the frame field $e_{\mu}^a$ and $\mathrm{SO}(3,1)$ spin connection $\omega_{\mu c}^b$ are independent variables. In the Hamiltonian formulation of ...
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1answer
144 views

Do Dirac field states belong to a Hilbert space with spinor coefficients?

The quantized Dirac field at a certain space-time point can be written (roughly) as a linear combination of creation operators acting on the Hilbert space of physical states, with coefficient that are ...
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Making sense of the canonical anti-commutation relations for Dirac spinors

When doing scalar QFT one typically imposes the famous 'canonical commutation relations' on the field and canonical momentum: $$[\phi(\vec x),\pi(\vec y)]=i\delta^3 (\vec x-\vec y)$$ at equal times ...
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Rigorous proof of Bohr-Sommerfeld quantization

Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In ...
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1answer
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Quantization from density of states

The density of states in quantum mechanics is obtained via the rather not so complicated relation below: $$\rho(E)=\delta (E-E_n)$$ Which means that if we know the energy quantization condition for a ...
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1answer
900 views

Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the ...
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Motivating Irreducibility of Hilbert Space for Quantization Axioms

In the context of geometric quantization, we usually look for a map from the Poisson algebra of classical observables to the algebra of quantum observables (or rather, a sub-algebra of the classical ...
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Classical Hamiltonian involving product of factors whose quantum analogues don't commute

Dirac remarked in his quantum mechanics book: One can usually assume that the Hamiltonian is the same function of the canonical coordinates and momenta in the quantum theory as in the ...
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