# Tagged Questions

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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### Is it a coincidence that quantum harmonic oscillators and photons have energy quantised as $E=hf$?

I have studied the quantum harmonic oscillator and solved the Schrodinger equation to find the eigen-energies given by $$E_n = \left(n+\frac{1}{2}\right)\hbar \omega.$$ Which means the energy ...
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### In quantum mechanics, how exactly do we associate Hermitian operators to classical observables? [duplicate]

In a first course on quantum mechanics, everybody learns some version of the following statement: Postulate: To every classical observable $A$ of a physical system, there corresponds a Hermitian ...
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### Is the standard model a quantized gauge theory?

I have studied some quantum field theory and gauge theory but I am definitely not an expert. I am aware that in quantizing electrodynamics one has to fix a gauge. I have read that for general gauge ...
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### Quantization of non-variational systems?

In undergraduate courses the introduction to Hamiltonian mechanics usually starts from a Newtonian view point. One has equations of motions of the form (not sure if it is ok to use covariant notation ...
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### What´s the physical foundation of the assumption that the curvature of spacetime can be quantised? [duplicate]

At the moment different paths (by percentual very few people in the world) are taken to arrive (that is, if an arrival exists) at a theory that can quantise the curvature of spacetime. Considering the ...
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### Geometric quantization of field theories and resulting statistics

Linear field theories Linear field theories form the classical counterparts to many important QFT's in condensed matter physics, modeling a wide range of materials, from the mundane (semiconductors), ...
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### Quantum systems without a classical analogue? [closed]

I am now reading the quantum mechanics textbook by Dirac (chap. 4, $\S21$, p. 88). He says that his quantization procedure does not include all possible systems in quantum mechanics and there are ...
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### An intuition on the Rindler modes

When we are solving the Klein-Gordon equation for the quantization of a massive scalar field on the Minkowski spacetime, we may use the global coordinates and obtain the usual quantization with plane ...
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### How to get anti-commuting rule from the view of field?

I was reading the 1951 Lectures on Advanced Quantum Mechanics and I found something really disturbing. That's the anti-commuting rule mentioned on Page 40 at last. Though it was named as Quantum ...
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### Quantization on Minkowski/Schwarzschild spacetimes based on unusual surface

I'm reading the book of Wald "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics", and I'm pondering on this problem: In Minkowski spacetime, we usually quantize our fields with ...
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### flux quantization in superconducting ring

I am trying to understand SQUID microscopy from the ground up, so I am starting with flux quantization in superconducting rings. I found a nice presentation that covers some of the details, but I am ...
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### In the Holometer experiment, why would one of the split laser beams arriving back at a slightly different time indicate the universe was quantized?

All the pop-sci articles I've read have a description of the set-up similar to this: It uses a pair of laser interferometers placed close to one another, each sending a one-kilowatt beam of light ...
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### Feynman Path Integral as a Quantization Scheme

Why isn't the path integral usually discussed as a quantization scheme, like geometric and deformation quantization? Was searching wikipedia for this.
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### How to impose canonical commutation relations when quantising a field

I believe this is a simple question, however I cannot find it explained anywhere what the term: "Impose canonical commutation relations" means. If I have a classical equation, and I wish to quantise ...
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### Regge trajectory and Kaluza Klein tower

The mass of hadrons in the Regge trajectory scales as $m=\sqrt{\frac{J}{\alpha}-\alpha_0}=\sqrt{\frac{n}{\alpha}-\alpha_0}\propto \sqrt{n}$, where $J=n$ is the spin of the particle (in natural units,...
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### $\pi$, $\sigma$ - atomic transitions with respect to the magnetic field axis

I am confused about the atomic transition with different polarized lights. I post the pictures as follows. There are four cases. In case 1, the right-handed circular polarized light ...
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### Questions about Quantization and Noncommutative Geometry

I am trying to orient myself among the vast amount of literature, trying to study the prerequisites necessary for gauge theory and theoretical physics. I have an undergraduate degree in mathematics ...
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### Why spurious pulses are likely in partial discharges?

My notes The gas multiplication in the proportional counters is based on the secondary ionization created in collisions between electrons and neutral gas molecules, resulting in some visible ...
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### Difference between discretization and quantization in physics

I am just trying to understand the fundamental difference between these two concepts in physics: From discreteness of some quantity: one usually interprets it as a quantity being only able to take ...
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### Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
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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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### What new does geometric or deformation quantization give to physics? [closed]

What new does geometric quantization or deformation quantization give to physics? For example: prediction of new physical phenomena or just better tool for quantization. What can these schemes do in ...
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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 $$\tilde{b}^i_{-\frac{1}{2}} |0\rangle_L \otimes b^j_{-\frac{1}{2}} |0\rangle_R.$$ It is ...
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### Discontinuity of paths in phase space path integrals

Berezin's famous paper "Feynman path integrals in a phase space" discusses the space of paths on which the phase space path integral is concentrated. In particular, these paths are known to be ...
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### 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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### Why is the introduction of a quantization volume necessary for quantization of the EM field

I have been working through the quantization of the electromagnetic field, and every source I find introduces a quantization volume with periodic boundary conditions in the process, in which we fit ...
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### How is quantization related to commutation? [duplicate]

How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence non-...
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### 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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### Canonical commutation relations in Light-cone gauge

It seems that when trying to identify the physical degrees of freedom for the string some authors$^1$ use: $$q^-=\frac{1}{\ell}\int_0^{\ell} X^-(\tau,\sigma)d\sigma$$ Then, the commutation relation ...
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### Volume factor in Faddeev-Popov quantisation

In Faddeev-Popov quantisation, why does the integral over gauge parameter cancel the volume factor of the gauge group that's in the denominator? In fact, I don't understand where the volume factor ...
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### What is “momentum density” and why it important to QFT?

I am reading Quantum Field Theory for the Gifted Amateur. On page 98, they provide a summary of a basic canonical quantization procedure: Step I: Write down a classical Lagrangian density in ...
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### How to associate a Hilbert space with a QM system?

I couldn't really find a fitting title for this question. I'm still relatively new to QM and am trying to get the basics down. I understand that a physical system is associated with a Hilbert Space, ...
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### Quantization conditions/ Real Scalar field

It is often written in books, the quantization conditions for classical field theory leading to Lagrangian of a real scalar field and thus to Klein Gordon equation. And these are introduced by ...
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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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### Classical Hamiltonian involving product of factors whose quantum analogues don't commute

Dirac remarked in his quantum mechanics book: One can usually assume that the Hamiltonian is the same function of the canonical coordinates and momenta in the quantum theory as in the ...