Why quantum field theory is not called quantum mechanics of changeable number particl

In summary, this book is not about quantum field theory as generally understood but about the relativistic quantum dynamics of point particles.
  • #1
ndung200790
519
0
Please teach me this:
Why we do not call the quantum field theory the quantum mechanics of a changeable number particles.Why we must use the term ''field''.I think that the indistinguish of identical particles,the dual particle-wave and changeable in number of particles mean the ''expansion'' characteristic.So it seem to me calling many particles quantum mechanics is enough.
Thank you very much in advanced.
 
Physics news on Phys.org
  • #2


ndung200790 said:
Please teach me this:
Why we do not call the quantum field theory the quantum mechanics of a changeable number particles.Why we must use the term ''field''.I think that the indistinguish of identical particles,the dual particle-wave and changeable in number of particles mean the ''expansion'' characteristic.So it seem to me calling many particles quantum mechanics is enough.
Thank you very much in advanced.

ndung, you have stolen my idea!

Seriously, I am with you on this point. I think that the main importance of QFT is not that it describes some mysterious "fields", but that it is a tool for studying systems with variable number of particles. Such particle-number-changing processes can be seen in particle collisions, decays, light emission and absorption, etc. To accommodate such systems one should use a Hilbert space in which the number of particles can vary from 0 to infinity. This is called the Fock space, and quantum mechanics in the Fock space can be called QFT.

Currently, there are lots of discussions of related issues in parallel threads, and you are welcome to join them:

https://www.physicsforums.com/showthread.php?t=474666

Eugene.
 
  • #3


Dear Sir.Eugene.Thank you very much for your useful book.This book will be help me very much in my studying quantum field theory.
Francis Xavier Nguyen Dung
 
  • #4


ndung, there are plenty of other fields of quantum mechanics which work with changable particle number. In principle, nearly everything formulated in terms of second quantization can deal with arbitrary particle numbers[1]. Note that this includes the majority of both solid state many-body physics (in particular the part working with lattice models or oder model systems) and quantum chemsitry.

Also, there is the whole statistical quantum mechanics business (with density operators and all), which also is intrinsically agnostic to the particle number.

QFT is really more about the conrete processes of creating and destroying particles, and their interrelations. For example, while in quantum chemistry you might describe an ionization which removes an electron from a system, the concrete process of ionization (say, interaction with light) is not typically handled; only the change in the electronic system due to the process.

[1] If the concrete particle number is known, of course only a specific N-particle sector of the Fock space is actually used.
 
  • #5


QFT is also extensively used in solid state physics where particle number is conserved.
 
  • #6


DrDu said:
QFT is also extensively used in solid state physics where particle number is conserved.

Yes, you are right. I forgot to mention that I was talking about fundamental relativistic quantum field theories that describe interactions between elementary particles, such as QED.

Eugene.
 
  • #7


meopemuk said:
Yes, you are right. I forgot to mention that I was talking about fundamental relativistic quantum field theories that describe interactions between elementary particles, such as QED.

Eugene.
Nevertheless a counter example is a counter example. I'd rather say that QFT is useful whenever you want to describe systems with different particle content on an equal footing. E.g. in ordinary nonrel. QM I have to set up a determinant for each N-particle state for each N. In QFT, the statistics is taken care by the commutation relations of the field operators. The only thing that changes with N is the eigenvalue of the number operator.
 
  • #8


Quantum field theory is called ''quantum field theory'' because its subject is quantum fields and their applications - of which particles are only one application, and a varying number of particles is not necessity in order to study systems of particles with field-theoretic methods.
ndung200790 said:
Thank you very much for your useful book.This book will be help me very much in my studying quantum field theory.
No. The book is not about quantum field theory as generally understood but about the relativistic quantum dynamics of point particles. The book presents a very narrow, idiosyncratic view of quantum field theory (and of relativity), and its study exposes you to a number of severe misunderstandings on the author's part (regarding the inequivalence of various relativistic forms of dynamics, and an interpretation of space-time resulting in spurious superluminal effects).

It can by no means replace studying standard quantum field theory books such as that of Weinberg (for the relativistic case) or statistical mechanics books such as that of Reichl (for the nonrelativistic case).
 
  • #9


But if we could derive a ''effective field'' from the point of view of quantum mechanics of particles,we would be able to solve the problem of renormalization in quantum gravity.So we would not need to use string theory.I think that to construct an ''effective field'' from a collection of changeable, interacting particles without the real existing field maybe easyer than to construct a complet string theory.
 
  • #10


DrDu said:
Nevertheless a counter example is a counter example. I'd rather say that QFT is useful whenever you want to describe systems with different particle content on an equal footing. E.g. in ordinary nonrel. QM I have to set up a determinant for each N-particle state for each N. In QFT, the statistics is taken care by the commutation relations of the field operators. The only thing that changes with N is the eigenvalue of the number operator.

This is a good point. I agree.

Eugene.
 
  • #11


How do you apply that definition to extending the classical mechanics of finite systems to classical fields?
 

1. Why is quantum field theory not called quantum mechanics of changeable number particles?

Quantum field theory is a mathematical framework used to describe the behavior of particles at a subatomic level. Unlike quantum mechanics, which deals with individual particles, quantum field theory considers the particles as excitations or disturbances in a quantum field. This means that the number of particles is not fixed, and can change over time, making the term "changeable number particles" misleading.

2. What is the difference between quantum field theory and quantum mechanics?

The main difference between quantum field theory and quantum mechanics is the level of abstraction. Quantum mechanics deals with individual particles and their properties, while quantum field theory deals with the behavior of these particles as excitations in a field. Additionally, quantum field theory is a more comprehensive and advanced theory that can describe the behavior of a large number of particles, while quantum mechanics is limited to a small number of particles.

3. Why is quantum field theory considered a more fundamental theory than quantum mechanics?

Quantum field theory is considered more fundamental because it provides a more comprehensive and accurate description of the behavior of particles at a subatomic level. It takes into account the principles of quantum mechanics, as well as relativity, and can describe the behavior of a large number of particles. In contrast, quantum mechanics is limited to describing the behavior of a small number of particles and does not take into account the effects of relativity.

4. Can quantum field theory explain all physical phenomena?

No, quantum field theory is not a complete theory and cannot explain all physical phenomena. While it is a powerful framework for understanding the behavior of particles at a subatomic level, it has limitations and does not yet fully incorporate the principles of gravity. It also does not provide a complete description of the universe at a large scale.

5. How is quantum field theory related to other theories, such as the Standard Model?

Quantum field theory is a mathematical framework that is used in many areas of theoretical physics, including the Standard Model. The Standard Model is a theory that describes the fundamental particles and their interactions based on the principles of quantum field theory. Other theories, such as quantum electrodynamics and quantum chromodynamics, are also based on the principles of quantum field theory.

Similar threads

  • Quantum Physics
Replies
1
Views
706
Replies
22
Views
2K
  • Quantum Physics
6
Replies
182
Views
10K
Replies
36
Views
3K
Replies
31
Views
2K
Replies
26
Views
2K
Replies
3
Views
1K
  • Quantum Physics
Replies
6
Views
360
  • Quantum Physics
Replies
4
Views
1K
Back
Top