First, second and third quantization formalisms

In summary, the conversation discussed the different quantization formalisms associated with Schrodinger's equation. First and second quantization are equivalent and deal with fermionic and bosonic symmetries, while third quantization is not as well-known. In QFT, there may be more significance placed on second quantization. Additionally, second quantization allows for a non-determinate number of particles, while first quantization does not. This may vary depending on the application.
  • #1
dpa
147
0
Hi all,

I was curious about mathematics and physical meaning behind first and second quantization formalisms of schrodinger's equation. what do these mean?

Okey, third quantization formalism may be weird/new for many but its associated with wheeler dewitt equation.
 
Physics news on Phys.org
  • #2
First&second quantization: There are different details associated with these names, depending on the field you are looking for.

When working with a finite or countably infinite Hilbert space as one-particle basis (on which the Fock spaces are expanded) and having a fixed number of particles[1], then first- and second quantization are entirely equivalent. The latter is then a reformulation of the former which intrinsically takes care of fermionic or bosonic symmetries (and by doing that makes dealing with determinants or permanents much easier). This is the form of second quantization you will encounter in many body physics of the condensed matter and chemical varieties, and there is really no mystery at all. However, my understanding is that in QFT, people tend to interpret more into second quantization, but I have never entirely understood how this differs from the straight-forward "normal" second quantization.

Of a third quantization I have never heard.

[1] Additonally, in second quantization you can have pure wave functions with a non-determinate number of particles, but in first quantization you cannot. How relevant this is depends on the application.
 
  • #3
See here for an advanced explanation.
 
  • #4
See here for an advanced explanation.

Well that was pretty easy to grab. :approve:

Uhh. well.. except for ... the ... you know that part with... everything! :frown:
 

What is the difference between first, second, and third quantization formalisms?

First quantization is the traditional approach to quantum mechanics, where a single particle is described by a wave function. Second quantization treats particles as excitations of quantum fields, allowing for the description of multiple interacting particles. Third quantization extends this to include the quantization of the space-time itself.

What are the advantages of using second and third quantization formalisms?

Second quantization allows for a more elegant and efficient description of many-particle systems, especially in the case of interacting particles. Third quantization provides a framework for studying the quantum properties of spacetime, which is crucial for understanding the early universe and black holes.

What are the limitations of first, second, and third quantization formalisms?

First quantization does not allow for the description of multiple interacting particles, making it difficult to study many-particle systems. Second and third quantization can be mathematically complex and may not be suitable for all types of problems.

How is the concept of particles treated differently in each quantization formalism?

In first quantization, particles are treated as distinct entities with a definite position and momentum. In second quantization, particles are treated as excitations of quantum fields, and their properties are described by operators. In third quantization, particles and their interactions are described as excitations of the space-time itself.

What are some real-world applications of first, second, and third quantization formalisms?

First quantization is the foundation for many modern technologies, such as transistors and lasers. Second quantization is used in many fields, including condensed matter physics, particle physics, and quantum chemistry. Third quantization has been applied to the study of black holes and the early universe, and has potential applications in quantum computing and quantum gravity.

Similar threads

Replies
3
Views
1K
  • Quantum Physics
Replies
4
Views
2K
  • Quantum Physics
Replies
3
Views
997
  • Quantum Physics
Replies
6
Views
1K
Replies
36
Views
4K
Replies
13
Views
2K
Replies
1
Views
2K
Replies
4
Views
817
  • Beyond the Standard Models
Replies
1
Views
3K
Back
Top