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Minute No. 4, the Quantum Field Theory
Quantum field theory Wei99 performs quantization of
classical fields in a very much the same way as the quantum mechanics
performs quantization of classical coordinates. The field wave
function now becomes a functional
of the field
, and the quantum fields and the quantum conjugate momenta
are

(13) 
where denotes the functional derivative. The Schrödinger equation
(9) now becomes the set of infinite number of differential
equations  a pretty complicated thing. I somehow hesitate to write
that the rest is just a technicality of how to solve it. In
principle, nothing special has happened. The same rules have been
applied and an analogous, albeit much more complicated, set of
equations emerged. However, we are very, very far from even
approaching a possibility of exact solutions of this set. We are not
at all going to embark on discussing these questions here. Basic
physical picture of the quantum field theory can be very well
discussed in terms of its classical counterpart, and in terms of
classicalfield Lagrangian densities discussed during the third
minute above. It as amazing how much can be said about properties of
the microworld by just specifying what are the symmetries and the
basic couplings between the classical fields. Below we follow this
way of presenting properties of strongly interacting systems.
The new, qualitatively different, element introduced by the quantum
field theory is that particles now disappeared from our description of
the physical world  there are only fields. One does not distinguish
which is the object that ``exists'' and which is the object that
``transmits forces''. All fields have both these characteristics
simultaneously; which field interacts with which, and in which way,
is fully specified by the Lagrangian density.
Next: Quantum Electrodynamics (QED)
Up: Quantum Field Theory in
Previous: Minute No. 3, the
Jacek Dobaczewski
20030127