|May10-10, 11:33 AM||#1|
Problems on quantum field operators in QFT
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!!!
|May10-10, 02:29 PM||#2|
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 so-called 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]
|May10-10, 06:02 PM||#3|
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