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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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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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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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 ...
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Pohlmeyer reduction of string theory for flat and AdS spaces

The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following: $ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
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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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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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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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Structure of Hilbert Space in Bosonic String Theory

My question is about the canonical quantization of free bosonic string theory as described by Green, Schwarz & Witten. There they use spurious states to calculate a value for the ambiguity ...
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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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Geometric quantization AND nuclear physics

Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. Geometric quantization is one formalization of the notion ...
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96 views

Pohlmeyer reduction of string theory for flat- and AdS- spaces

The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following: $ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
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273 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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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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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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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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81 views

Why is commutation relations the first step in quantization?

Why is commutation relations the first step in quantization?
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Noncommutative Field Quantization

I'm studying noncommutative (quantum) field theory, and I have confusion need to be clear. I'm reading Szabo's and Douglas's .pdf of noncommutative QFT. As I understand, in the book they just ...
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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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126 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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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 ...
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38 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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34 views

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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Quantization in a 2D quasicrystal?

let be the Schroedinger equation with a potential in a quascristal $$ -( \partial _{x}^{2}+ \partial _{y}^{2}) \Psi (x,y)+ V(x,y)=E_{n} \Psi (x,y) $$ if we were in a crystal we could impose the ...
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quantization with a pure exponential potential

Given the Hamiltonian $$ H=p^{2}-ge^{-x}, $$ are the energies negative? If I impose the boundary condition $y(0)=0$ and $y(\infty)=0$, I get the condition for the energies $$ J_{2i \sqrt{E(n)}}(g) ...