# From quantum field theory to quantum mechanics

1. Sep 29, 2009

### luxxio

i need references on the topics. thanx

2. Sep 29, 2009

### meopemuk

luxxio,

the answer depends on your definition of the term "quantum mechanics". There is a broad definition of this term and a narrow one.

In the broad definition "quantum mechanics" is a theory operating with Hilbert spaces, wave functions, Hermitian operators, etc. In this case, there is no separation between QFT and QM. QFT is simply a particular case of the general quantum mechanical formalism.

In the narrow definition "quantum mechanics" is a quantum theory describing systems with fixed numbers of particles. In this case the answer is not that simple, because the number of ("bare") particles in any QFT system (including the vacuum and 1-particle systems) is changing all the time: virtual particles and pairs are constantly emitted and absorbed. The best explanation of how the traditional QM with fixed number of particles follows from the QFT (where the number of particles is not fixed) can be found in the "dressed particle" formalism:

O. W. Greenberg and S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim. 8 (1958), 378.

You can use Google Scholar to find more recent references to this rather old idea.

Last edited: Sep 29, 2009
3. Sep 29, 2009

### RUTA

If you want the path integral counterpart to the Schrodinger Equation from the transition amplitude of QFT, see Chapter 1 of Zee, A.: Quantum Field Theory in a Nutshell. Princeton University Press, Princeton (2003).

4. Sep 29, 2009

### ice109

5. Sep 29, 2009

### Born2bwire

I picked up that book just the other day and I agree that it is a good introductory source from what I have seen of the first couple of chapters. Feynman's Path Integral text is also a very good reference but it seems that it only had one printing so it may be difficult to get.