The quantization tag has no wiki summary.
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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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0answers
87 views
How functions become operators in quantum mechanics? [duplicate]
What used to be functions in the context of classical mechanics like position, linear momentum, angular momentum, etc in quantum mechanics are operators (these operators act on the state to get ...
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1answer
83 views
Quantum Theory as a framework for other theories of nature
We know that Quantum Theory should be considered as a framework in which all other theories/forces (Strong, Weak, EM and Gravity) exist.
For example, we have the Quantum Chromodynamics, Quantum ...
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1answer
93 views
Grassmann fields according to Peskin and Schroeder
On page 301 in Peskin and Schroeder, they claim that a Grassman field $\psi(x)$ may be decomposed as
$$\psi(x) = \sum_i c_i \phi_i(x),$$
where the $c_i$ are Grassmann numbers and the $\phi_i$ are ...
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1answer
95 views
Quantization Surface in QFT
What does the Quantization Surface mean here?
Reference: H. Latal W. Schweiger (Eds.) - Methods of Quantization
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5answers
305 views
What is Quantization?
In classical mechanics you construct an action (involving a Lagrangian in arbitrary generalized coordinates, a Hamiltonian in canonical coordinates [to make your EOM more "convenient & ...
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1answer
161 views
What fundamental reasons imply quantization?
In classical wave mechanics, quantization can occur simply from a finite potential well.
In quantum mechanics, the quantization is obtained from the Schrödinger equation, which is, to my knowledge, a ...
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2answers
125 views
Central charge in a $d=2$ CFT
I've always been confused by this very VERY basic and important fact about two-dimensional CFTs. I hope I can get a satisfactory explanation here. In a classical CFT, the generators of the conformal ...
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1answer
103 views
Does string/M-theory address higher-dimensional membrane vibration modes?
A loop is a 1-sphere that can vibrate in increasingly complex ways as it is embedded in higher dimensional spaces.
Does string theory assume that 1-spheres are the only possible vibrating ...
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2answers
138 views
The Quantization of Photon Energies
Despite Planck's constant being in $E=hf$, it would appear to me that energy is still not discrete, as frequency can be an fraction of a Hertz that one wants. How does this imply that electromagnetic ...
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0answers
33 views
quantization with constraints
let be a Hamiltonian system $ H= H(x,p) $
for this system there is a conserved quantity namely $ C=xp $ so the total system is invariant under rotation
if we 'quantizy' this function $ ...
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1answer
116 views
Reason behind canonical quantization in QFT?
Reason behind canonical quantization in QFT?
In the scalar field theory we simply promote the scalar field, $\phi(x)$ to a set of operators: $\hat{\phi}(x)$. What is the reason behind this?
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1answer
138 views
What object is quantized in quantum gravity?
In theories of quantum gravity, which object is it that is quantized?
Working on field theories, I expect the quantization to mean the promotion of a classical field to an operator valued field that ...
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3answers
227 views
Fundamentals of Quantum Electrodynamics
In quantum electrodynamics, the classical Hamiltonian is obtained from the classical electromagnetic Lagrangian. Then the classical electric and magnetic fields are promoted to operators, as is the ...
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1answer
120 views
Does the Renormalization of QFT Contradict Canonical Quantization?
Does the renormalization of QFT contradict canonical quantization?
In canonical quantization, you take the classical fields and canonical momenta and turn them into operators, and you require that ...
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0answers
124 views
The correspondence between Poisson bracket and Commutators in Quantum Mechanics
I don't understand canonical quantization. In passing from classical to quantum, one replaces the Poisson brackets with the commutators. I don't really understand this.
How can we generally show that ...
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0answers
88 views
Quantization as a functor
Can anyone give an mathematical elaboration of the following statement:
Quantization is a functor carrying the category of Hilbert space and linear maps to that of Symplectic manifolds satisfying ...
5
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1answer
104 views
Quantum master equation in the Batalin-Vilkovisky formalism
I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift $\delta\Psi[\chi]$ in $\Psi[\chi]$, we have
$$
\begin{split}
\delta ...
4
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1answer
234 views
Bohr-Sommerfeld quantization from the WKB approximation
How can one prove the Bohr-Sommerfeld quantization formula
$$ \oint p~dq ~=~2\pi n \hbar $$
from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation?
With $S$ the ...
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1answer
134 views
Critical dimension in quantization of p-branes
So I have what might be a fairly basic question, but my understanding that in the quantization of the the string, or the 1-brane, there are conditions on the number of spacetime dimensions to ensure ...
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2answers
166 views
Integer physics
Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
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Do semiclassical GR and charge quantisation imply magnetic monopoles?
Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how?
(I am not ...
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1answer
115 views
What is the action for an electromagnetic field if including magnetic charge
Recently, I try to write an action of an electromagnetic field with magnetic charge and quantize it. But it seems not as easy as it seems to be. Does anyone know anything or think of anything like ...
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2answers
469 views
Weyl Ordering Rule
While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian ...
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1answer
107 views
State space of QFT, CCR and quantization, and the spectrum of a field operator?
In the canonical quantization of fields, CCR is postulated as (for scalar boson field ):
$$[\phi(x),\pi(y)]=i\delta(x-y)\qquad\qquad(1)$$
in analogy with the ordinary QM commutation relation:
...
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0answers
19 views
Allowed Quantum States- Filkelstein and Rubinstein constraints
So basically i'm doing a report on Finkelstein and Rubinstein constraints. I have a system where the allowed quantum states satisfy ...
12
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2answers
535 views
Why one-dimensional strings, but not higher-dimensional shells/membranes?
One way that I've seen to sort-of motivate string theory is to 'generalize' the relativistic point particle action, resulting in the Nambu-Goto action. However, once you see how to make this ...
5
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2answers
141 views
Quantization of strings on a curved backgrond
usually when people want to quantize the string on flat background, they will try to find the the OPE of embeddings (by solving a green function in a 2D space) and use them to find the energy-momentum ...
7
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1answer
240 views
Canonical quantization in supersymmetric quantum mechanics
Suppose you have a theory of maps
$\phi: {\cal T} \to M$
with $M$ some Riemannian manifold,
Lagrangian
$$L~=~ \frac12 g_{ij}\dot\phi^i\dot\phi^j + \frac{i}{2}g_{ij}(\overline{\psi}^i ...
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7answers
835 views
Is the quantization of gravity necessary for a quantum theory of gravity?
The other day in my string theory class, I asked the professor why we wanted to quantize gravity, in the sense that we want to treat the metric on space-time as a quantum field, as opposed to, for ...
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0answers
76 views
Geometric quantization of a hydrogen atom
I want to know how to quantize a hydrogen atom as an example of geometric quantization. Apparently there is a derivation in the book "Geometric Quantization in Action: Applications of Harmonic ...
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4answers
232 views
What entities in Quantum Mechanics are known to be “not quantized”?
Since all the traditional "continuous" quantities like time, energy, momentum, etc. are taken to be quantized implying that derived quantities will also be quantized, I was wondering if Quantum ...
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1answer
401 views
exponential potential $ \exp(|x|) $
For $a$ being positive what are the quantisation conditions for an exponential potential?
$$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$
with boundary conditions $$ y(0)=0=y(\infty) $$
I ...
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2answers
214 views
Definition of “Quantizing”
Could anyone explain to me what "quantize" means in the following context?
Quantize the 1-D harmonic oscillator for which
$$H~=~{p^2\over 2m}+{1\over 2} m\omega^2 x^2.$$
I understand that the ...
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1answer
230 views
Operator Ordering Ambiguities
I have been told that $$[\hat x^2,\hat p^2]=2i\hbar (\hat x\hat p+\hat p\hat x)$$ illustrates operator ordering ambiguity.
What does that mean?
I tried googling but to no avail.
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When can photon field amplitudes be written as field operators?
Suppose I have some classical field equation for two photon fields with amplitudes $A_1(z),A_2(z)$ (plane waves) given as
${A}_1=\alpha f(A_1,A_2) \\
{{A}_2}=\beta g(A_1,A_2) $
Under what ...
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1answer
232 views
Quantization of Nambu–Goto action in multiples of Planck's constant?
Isn't it possible? Quantization of Nambu–Goto action
$$\mathcal{S} ~=~ -\frac{1}{2\pi\alpha'} \int \mathrm{d}^2 \Sigma \sqrt{{\dot{X}} ^2 - {X'}^2}~=~nh\qquad n \in\mathbb{Z}.$$
3
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1answer
134 views
Poincaré group on quantum Klein-Gordon field (C*-algebraic scenario)
on the same topic as this question, I have been trying to fool around with the free real K-G field in flat spacetime on the C*-algebraic scenario (Haag-Kastler axioms, Weyl quantization, etc).
Since ...
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2answers
352 views
Path integral and geometric quantization
I was wondering how one obtains geometric quantization from a path integral. It's often assumed that something like this is possible, for example, when working with Chern-Simons theory, but rarely ...
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4answers
685 views
Reason for the discreteness arising in quantum mechanics?
What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
3
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2answers
171 views
Ordering Ambiguity in Quantum Hamiltonian
While dealing with General Sigma models (See e.g. Ref. 1)
$$\tag{10.67} S ~=~ \frac{1}{2}\int \! dt ~g_{ij}(X) \dot{X^i} \dot{X^j}, $$
where the Riemann metric can be expanded as,
$$\tag{10.68} ...
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1answer
180 views
Equivalence of classical and quantized equation of motion for a free field
Suppose a classical free field $\phi$ has a dynamic given in Poisson bracket form by $\partial_o\phi=\{H, \phi\}$. If we promote this field to an operator field, the dynamic after canonical ...
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0answers
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Quantization and natural boundary conditions
The Euler-Lagrange equations follow from minimizing the action. Usually this is done with fixed (e.g. vanishing) boundary conditions such that we do not have to worry about any boundary terms. ...
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1answer
222 views
When can a classical field theory be quantized?
Given a classical field theory can it be always quantized? Put in another way, Does there necessarily need to exist a particle excitation given a generic classical field theory? By generic I mean all ...
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2answers
342 views
Dirac equation as canonical quantization?
First of all, I'm not a physicist, I'm mathematics phd student, but I have one elementary physical question and was not able to find answer in standard textbooks.
Motivation is quite simple: let me ...
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2answers
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Bohr Model of the Hydrogen Atom - Energy Levels of the Hydrogen Atom
Why the allowed (stationary) orbits correspond to those for which the orbital angular momentum of the electron is an integer multiple of $\hbar=\frac {h}{2\pi}$?
$$L=n\hbar$$
Bohr Quantization rule of ...
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2answers
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quantization of this hamiltonian?
let be the Hamiltonian $ H=f(xp) $ if we consider canonical quantization so
$ f( -ix \frac{d}{dx}-\frac{i}{2})\phi(x)= E_{n} \phi(x)$
here 'f' is a real valued function so i believe that $ f(xp) $ ...
3
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1answer
286 views
Dirac's quantization rule
I first recall the Dirac's quantization rule, derived under the hypothesis that there would exit somewhere a magnetic charge: $\frac{gq}{4\pi} = \frac{n\hbar}{2} $ with $n$ natural.
I am wondering ...
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983 views
Why do we use Planck's constant?
I have been trying to reason why energy packets (i.e. photons) are assumed to be quantized. I know this originated from Max Planck, but may someone explain why energy couldn't be emitted continuously ...
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Generalizing Heisenberg Uncertainty Priniciple
Writing the relationship between canonical momenta $\pi _i$ and canonical coordinates $x_i$
$$\pi _i =\text{ }\frac{\partial \mathcal{L}}{\partial \left(\frac{\partial x_i}{\partial t}\right)}$$
...
