
#1
May1010, 11:33 AM

P: 21

Hello!
I met some annoying problems on quantum field operators in QFT.They are as follows: (1)The quantum field operator( scalar field operator, for example),is often noted as φ（r,t). Can it be interpreted as like this: φ（r,t) is the coordinate represetation of a more abstract,theoretical operator φ in Hilbert space? (2)Is there exist the represetation(such as momentum, coordinate.....) which is similar to that in quantum mechanics in QFT? Thanks for reply!!! 



#2
May1010, 02:29 PM

Sci Advisor
P: 5,307

Regarding 1) no, r is an "index", not an entity living in a Hilbert space. This becomes clear if one derives quantum field theory of a scalar field from infinitly many coupled harmonic oscillators.
Regarding 2) yes, these are the socalled creation an annihilation operators obtained by Fourier transform of the field operators, usually denoted as [tex]a^\dagger(p)[/tex] and [tex]a(p)[/tex] 



#3
May1010, 06:02 PM

P: 21




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