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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What makes background gauge field quantization work?

[Again I am unsure as to whether this is appropriate for this site since this is again from standard graduate text-books and not research level. Please do not answer the question if you think that ...
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Question about the parity of the ghost number operator in BRST quantization

Given a Lie algebra $[K_i,K_j]=f_{ij}^k K_k$, and ghost fields satisfying the anticommutation relations $\{c^i,b_j\}=\delta_j^i$, the ghost number operator is then $U=c^ib_i$ (duplicate indices are ...
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Trouble with constrained quantization (Dirac bracket)

Consider the following peculiar Lagrangian with two degrees of freedom $q_1$ and $q_2$ $$ L = \dot q_1 q_2 + q_1\dot q_2 -\frac12(q_1^2 + q_2^2) $$ and the goal is to properly quantize it, following ...
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Can symmetry generators be used for quantization?

Take the Poincaré group for example. The conservation of rest-mass $m_0$ is generated by the invariance with respect to $p^2 = -\partial_\mu\partial^\mu$. Now if one simply claims The state where ...
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Can Fermionic symmetries be fully integrated into geometric deformation complexes or symplectic reduction?

How should a geometer think about quotienting out by a Fermionic symmetry? Is this a formal concept? A strictly linear concept? A sheaf theoretic concept? How does symplectic reduction work with odd ...
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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 ...
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7answers
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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 ...
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Phonons in non-crystalline media

Do sound waves in a gas consist of phonons? What about a glass? Or other non-crystalline materials such as quasicrystals? How does the lack of translational symmetry affect the quantization of the ...
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8answers
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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 ...
6
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2answers
497 views

How do we resolve operator ordering ambiguities when quantizing generic nonlinear second-class constraints?

Dirac came up with a general theory of constraints, including second-class constraints. To quantize such systems, he first computed the Dirac bracket classically, and only then "promoted" the ...
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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 ...
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792 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 ...
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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 ...
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1answer
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Possibly naive question about quantized space-time

I beg your pardon in advance if this question is naive. In Quantum Mechanics, discrete values of measurements occur only in relation to bound states. This is because of the general solution for the ...
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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 ...