Re: please help my confusion about particles and irreps.
Igor Khavkine wrote:
But we are getting farther and farther from the topic. This subthread is
about the relative merits of the field and particle formulations. So on
topic, let me throw someting else into the mix. The mathematical
formulation of QFT can handle a large variety of theories, with or
without symmetries. Take for instance a quantum field interacting with a
time and space varying external field. There is neither space nor time
translation symmetry in this theory. So particle states cannot be
identified as eigenstates of any sort of symmetry generators. However, a
satisfactory quantization can be constructed by solving partial
differential equations for the wave functions obtained as matrix
elements of field operators. And yes, such a model has numerous physical
applications.
Again, I would prefer to limit our discussion to straight QED.
If we remove philosophical noise, then the question boils down to this:
is it better to represent operators in the Fock space as functions of
quantum fields or as functions of creation/annihilation operators of
particles? Strictly mathematically, these two representations are
interchangeable: fields can be uniquely obtained from particle operators
and vice versa. Then we can ask which way is more convenient and
physically transparent?
If we speak about traditional QED which is interested, almost
exclusively, in the S-matrix, then fields are certainly more
convenient. Scattering amplitudes can be obtained
from Feynman rules that can be read directly from the Lagrangian.
These formulas involve propagators that are expectation values of
field products. For these calculations one even does not need an
explicit expression for the Hamiltonian.
Of course, the same results could be obtained by using interaction
terms in the Hamiltonian expressed through creation and annihilation
operators. But this involves much more labor and, understandably,
is not popular.
The story is different if we try to calculate the time evolution.
For that, we need the Hamiltonian in the "dressed particle"
representation. The "dressing transformation" requires sorting
of different operators into three groups: renorm, phys, and unphys.
Operators in these groups are most easily identified by their
composition in terms of creation and annihilation operators.
For example
a^*a is renorm
a^*ac is unphys
a^*a^*aa is phys.
So, for time evolution and bound states calculations in RQD,
the representation in terms of creation and annihilation operators
is certainly more preferable.
Eugene.
.
Relevant Pages
- Re: Finite time calculation in QED
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(sci.physics.research) - Re: Finite time calculation in QED
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(sci.physics.research) - Re: Big Bang Theroists
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(sci.crypt) - Re: How real are the "Virtual" partticles?
... > is not a physical state. ... time evolution in QED without using the dressed particle approach. ... I know two ways that allow to compute the time evolution. ... Another way is to use dressed particle Hamiltonian H_d and keep ...
(sci.physics.research) |
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