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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.

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 instead.

356 questions
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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 quantum field theory on curved space-time would…
MBN
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59
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6 answers

What is the "secret " behind canonical quantization?

The way I (and perhaps most students around the world) 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 theory, which is based on the rule of transforming…
Jacob
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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 $x^\mu$), which is then projected into the space…
Tobias Kienzler
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3 answers

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 physics to be preserved. But nevertheless the…
user1355
42
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2 answers

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 I am not yet quite fluent in string theory). But…
Marek
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7 answers

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 boundary conditions, and the quanta in harmonic…
user7757
33
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3 answers

Why does non-commutativity in quantum mechanics require us to use Hilbert spaces?

I am reading Why we do quantum mechanics on Hilbert spaces by Armin Scrinzi. He says on page 13: What is new in quantum mechanics is non-commutativity. For handling this, the Hilbert space representation turned out to be a convenient — by many…
Stan Shunpike
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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 transformation satisfy the Witt algebra $$[…
Prahar
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3 answers

How to derive the formula for the quantum Hamiltonian $\hat H(\hat P,\hat Q)$ in terms of the classical $H(q,p)$, via Weyl Ordering?

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 $H(p,q)$ by $$\hat{H}(\hat{P},\hat{Q}) \equiv \int…
rainman
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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.
Greta
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Why aren't the energy levels of the Earth quantized?

The Hamiltonian of the Earth in the gravity field of the Sun is the same as that of the electron in the hydrogen atom (besides some constants), so why are the energy levels of the Earth not quantized? (of course the question is valid for every mass…
Jacob
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5 answers

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 example, just leaving the metric alone, and doing…
Jonathan Gleason
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Quantization of a particle on a spherical surface

Suppose we have a particle of mass $m$ confined to the surface of a sphere of radius $R$. The classical Lagrangian of the system is $$L = \frac{1}{2}mR^2 \dot{\theta}^2 + \frac{1}{2}m R^2 \sin^2 \theta \dot{\phi}^2 $$ The canonical momenta are…
Jiang-min Zhang
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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 'generalization', it becomes obvious how to write down…
Jonathan Gleason
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7 answers

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 so since I am confused.
user403
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