What is the paraquantization? How does one develop a geometric pq?

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In summary, the conversation is about paraquantization and its relation to geometric paraquantization and tri commutation relations of parastatistical particles. The method of paraquantization does not use standard commutation relations between position and momentum. The reference mentioned is an article by H. S. Green from 1953. The person asking the question is from Kongoo and does not have access to an e-library. They are interested in finding the article and other related work on "anyons."
  • #1
theyazen
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hi this is my first participation in this forum
I want aske some quastions
what is the paraquantization ?
can we devloppe a geometric paraquantization?
how can demonstrate that the green anzats is equivalent to tri commutation relation of parastatistical particle
 
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  • #2
theyazen said:
what is the paraquantization ?

Apparently, it is a method of quantization which does not use the standard commutation relations between position and momentum. Maybe this reference will be useful: H. S. Green, Phys. Rev. 90, (1953) 270.
 
  • #3
thenk you
but where can I find this article because I am from kongoo I have not the acces to e librery
 
  • #4
theyazen said:
thenk you
but where can I find this article because I am from kongoo I have not the acces to e librery

You could find it in a reglular library perhaps... but anyways, I attached the article. You might also be interested in work done on "anyons" in the late 70s and afterwards.
 
  • #5
hmm... is it attached? I tried to attach the .pdf, but I don't see it.
 
  • #6
thank you and I wait the article
 

FAQ: What is the paraquantization? How does one develop a geometric pq?

What is paraquantization?

Paraquantization is a mathematical framework used to describe and analyze the behavior of systems with both classical and quantum properties. It combines elements of classical mechanics and quantum mechanics to provide a more complete understanding of physical systems.

How does paraquantization differ from traditional quantization?

Traditional quantization is based on the canonical quantization method, which involves replacing the classical Poisson brackets with commutation relations between operators. Paraquantization, on the other hand, uses a noncommutative product known as the para-product to replace the classical product in the Hamiltonian equations.

What are the advantages of using paraquantization?

One of the main advantages of paraquantization is that it allows for a unified treatment of classical and quantum dynamics. It can also provide a more accurate description of physical systems that exhibit both classical and quantum behavior, such as mesoscopic systems.

How does one develop a geometric pq?

Developing a geometric pq involves constructing a para-Hamiltonian structure on a symplectic manifold. This is done by defining a para-product on the tangent bundle of the manifold and using it to define a para-Hamiltonian function. The resulting equations of motion will then describe the dynamics of the system in terms of para-Hamiltonian vector fields.

What are some applications of paraquantization?

Paraquantization has many applications in physics, including in the study of quantum field theory, quantum gravity, and condensed matter systems. It also has applications in mathematical fields such as noncommutative geometry and deformation quantization.

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