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

[ndung200790]

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.

 

[meopemuk]

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.

 

[ndung200790]

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

 

[cgk]

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.

 

[DrDu]

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

 

[meopemuk]

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.

 

[DrDu]

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.

 

[A. Neumaier]

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.

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).

 

[ndung200790]

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.

 

[meopemuk]

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.

 

[C. H. Fleming]

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