# What is the difference between second quantization and QFT?

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• fxdung
In summary, second quantization is a method of using field theoretic techniques to describe the non-relativistic quantum mechanics of many identical particles, while QFT takes the opposite approach and starts with quantum fields as the fundamental objects.
fxdung
Please teach me the difference between second quantization and QFT?

Demystifier
Second quantization is an equivalent language for describing non-relativistic quantum mechanics of many identical particles, which can also be described in "first quantized form" using the Schroedinger equation found in introductory textbooks. In other words, second quantization is a way of using field theoretic methods to describe the non-relativistic quantum mechanics of many identical particles.

Terminology is not very strict, and there are other usages of the term.

fxdung said:
Please teach me the difference between second quantization and QFT?
The difference is more philosophical than physical. In second quantization one starts from particles as basic primitive objects and then develops mathematical tricks for efficient description of many-particle states obeying either Bose-Einstein or Fermi-Dirac statistics. These mathematical tricks can be written in terms of abstract mathematical objects called quantum fields. In QFT one starts from quantum fields as basic primitive objects and then derives that certain quantum states of those fields can be interpreted as particles obeying either Bose-Einstein or Fermi-Dirac statistics. In short,

second quantization: particles ##\rightarrow## fields
QFT: fields ##\rightarrow## particles

bhobba and nrqed

## 1. What is second quantization and how is it different from QFT?

Second quantization is a mathematical framework used to describe the behavior of many-particle systems, such as atoms and molecules. It involves treating particles as excitations of quantum fields. QFT, on the other hand, is a theoretical framework used to describe the behavior of particles and their interactions in terms of quantum fields. The main difference between the two is that second quantization focuses on the behavior of many particles, while QFT focuses on the behavior of individual particles.

## 2. Can second quantization and QFT be used interchangeably?

No, second quantization and QFT are not interchangeable. While they both use the concept of quantum fields, they have different purposes and applications. Second quantization is used to describe many-particle systems, while QFT is used to describe the behavior of individual particles and their interactions.

## 3. How does second quantization relate to quantum mechanics?

Second quantization is a mathematical formalism that extends the principles of quantum mechanics to systems with many particles. It allows for a more efficient and systematic way of describing the behavior of many particles compared to traditional quantum mechanics. QFT, on the other hand, is considered to be a more fundamental theory that incorporates quantum mechanics and special relativity.

## 4. Is second quantization necessary for understanding QFT?

Yes, second quantization is a necessary mathematical tool for understanding QFT. It provides a formalism for describing the behavior of quantum fields, which are essential to the foundations of QFT. Without second quantization, it would be difficult to fully grasp the concepts and calculations involved in QFT.

## 5. Are there any real-world applications of second quantization and QFT?

Yes, both second quantization and QFT have a wide range of applications in various fields, including condensed matter physics, particle physics, and quantum chemistry. They are used to understand and predict the behavior of complex systems and have been instrumental in the development of new technologies, such as transistors and lasers.

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