The basic objects in quantum field theory

The standard model is a quantum field theory. These theories are called
so after the basic objects in them: Quantum fields.

In quantum field theory, particles are not the basic objects,
but are derived features inherent in quantum fields:
Particles are the localized excitations of quantum fields with
well-define quantum numbers.

In standard quantum field theory, particles are asymptotic objects,
existing only before and after collisions. Then they have definite
properties, including a real mass -- one says they are on-shell.
Decaying excitations can be treated in some approximation as such
asymptotic objects if they are long-living enough; these are the
unstable particles. Their mass is uncertain by an amount inversely
proportional to their lifetime. Indeed, mass and lifetime are combined
into a complex mass, which is the characterizing parameter as it is a
pole of the S-matrix of the system.
If particles do not live long enough to be observed directly,
they still manifest themselves as resonances.
(Sometimes, one says that unstable particles are off-shell. But this
meaning of off-shell should not be confused with the off-shell notion
for virtual particles, where mass m is real but momentum p is not
restricted to satisfy the mass shell equation p^2=m^2 as for stable
particles. Observable unstable particles are not virtual.)

During collisions, there is the quantum field, but there are no
discernible particles. Depending on the ways the quantum field is
analyzed, one may ascribe parts of the fields to certain particles.
In schemes that do so, these particles are thought to be free
(although they cannot be, which results in renormalization problems);
they are called virtual particles, and correspond to the internal
lines of corresponding Feynman diagrams. They are off-shell, and
different schemes for analyzing the quantum field during a collision
assign different portions of the field to different and differently
interacting virtual particles. Nonperturbative schemes such as lattice
gauge theory do not permit such an analysis in terms of virtual
particles. Thus the presence and meaning of virtual particles is
scheme-dependent, and one cannot ascribe any objective reality to them.

In a scattering experiment that does not change the number and type of
particles, the in-going particles become virtual (and off-shell) in
perturbative schemes until the interaction is completed, when they
are recognizable again as a real, on-shell particle.

In a dense medium, collisions are so frequent that the asymptotic regime
needed for the preceding interpretations to make sense is never
achieved. However, using nonperturbative techniques such as the
closed-time path integral, one can define quasiparticles with
position-dependent masses (on-shell in Boltzmann-type equations,
off-shell in Kadanoff-Baym-type equations) that satisfy a quantum
kinetic equation with measurable consequences.
These quasiparticles are real and measurable.

Indeed, from a fundamental point of view, most particles (all apart
from leptons, quarks and gluons), and in particular the proton and
the neutron, must be considered as quasiparticles.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ