The quantization tag has no wiki summary.
13
votes
8answers
998 views
What are the reasons to expect that gravity should be quantized?
What I am interested to see are specific examples/reasons why gravity should be quantized. Something more than "well, everything else is, so why not gravity too". For example, isn't it possible that a ...
15
votes
3answers
869 views
How general is the Lagrangian quantization approach to field theory?
It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of ...
9
votes
1answer
732 views
Why does gravity need to be quantised?
The electroweak and strong forces seem to be completely different types of forces to gravity. The latter is geometric while the former are not (as far as I'm aware!). So why should they all be ...
12
votes
4answers
586 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 ...
14
votes
1answer
656 views
How does classical GR concept of space-time emerge from string theory?
First, I'll state some background that lead me to the question.
I was thinking about quantization of space-time on and off for a long time but I never really looked into it any deeper (mainly because ...
7
votes
0answers
143 views
Magnetic monopole and electromagnetic field quantization procedure
From the Maxwell's equations point of view, existence of magnetic monopole leads to unsuitability of the introduction of vector potential as $\vec B = \operatorname{rot}\vec A$. As a result, it was ...
15
votes
7answers
1k views
Does Quantum Mechanics assume space and time are continuous?
I was confused when I was listening to a Quantum Mechanics lecture online. Are space and time assumed to be continuous or discrete in Quantum Mechanics?
I can see the question is vague, but this is ...
3
votes
2answers
858 views
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 ...
14
votes
7answers
613 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 ...
10
votes
1answer
417 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 ...
1
vote
1answer
199 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
votes
1answer
303 views
Canonical quantization of quantum field
The canonical quantization of a quantum field prescribes that given a lagrangian, one can quantize the theory by imposing the commutation relations between the field operators and their conjugated ...
5
votes
3answers
362 views
Are there any quantities in the physical world that are inherently rational/algebraic?
Whenever we measure something, it is usually inexact. For example, the mass of a baseball will never be measured exactly on a scale in any unit of measurement besides "mass in baseballs that are ...
21
votes
9answers
2k 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 ...
7
votes
1answer
202 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
$$L~=~ \frac12 g_{ij}\dot\phi^i\dot\phi^j + \frac{i}{2}g_{ij}(\overline{\psi}^i ...
3
votes
1answer
87 views
State space of QFT, CCR and quantization, and the spectrum of a field operator?
In the canonical quantization of fields, CCR is postulated as (for scalar boson field ):
$$[\phi(x),\pi(y)]=i\delta(x-y)\qquad\qquad(1)$$
in analogy with the ordinary QM commutation relation:
...
4
votes
1answer
91 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 ...
5
votes
0answers
80 views
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 ...
5
votes
2answers
201 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 ...
1
vote
1answer
85 views
understanding the oscillating part of the Gutzwiller trace
given the density of states according to Gutzwiller's trace formula
$ g(E)= g_{smooth}(E)+ g_{osc}(E) $
i know that the 'smooth' part comes from $ g_{smooth}(E)= \iint dxdp \delta(E-p^{2}-V(x)) $ ...
1
vote
0answers
70 views
shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula
shouldn't be the quantization formula (in one dimension) equal to
$ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ??
where the Oscillating term is just the correction from Gutzwiller trace formula or a ...
9
votes
3answers
391 views
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 ...
3
votes
1answer
234 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 ...
