The term "particle" is used to denote an identifiable constituent of matter or energy. Here "identifiable" means that the characteristics of one type of particle allow it to be distinguished from another type of particle which differs in at least one of those characteristics. It does not imply that two particles with the same characteristics are distinguishable. In fact, unless they are spacelike separated, two particles of the same type cannot be distinguished, nor can they even be said to be two different particles. This is due to their "field" nature.
A field is something which has one or more characteristics at every event in spacetime. The types of characteristics are determined by the symmetry group which the field represents. Hence the electron field has characteristics of mass, momentum, spin, electric charge, helicity and isospin, since it represents an object which can transform under the Poincare Group and the "internal" group U(1) charge x SU(2) left-handed isospin. Note that we say the electron field; since a field has a domain of all of spacetime, a single field must describe all particles with the same characteristics. In fact, by defining a field (often called the "vacuum") which has all possible particle characteristics, one can describe the entire universe of matter and energy with a single field (which is of course useless for computational purposes, but absolutely necessary when we consider that any two timelike separated particles are interacting). What then distinguishes the vacuum from a particle?
Each characteristic of the field may have two or more values associated with it (for instance, mass has an apparently continuous spectrum of positive real numbers associated with it, while spins must be positive or negative half integers or zero). Since many of these values are discrete in nature, they are called "quantum numbers". If we can identify the quantum numbers of the vacuum (which we define as absent of particles), then field values which differ from those are called "excitations" or "quanta". Note that the definition of the vacuum quantum numbers depends on the spacetime frame of reference, since one of the symmetry groups of the vacuum is shared by the spacetime manifold. The quanta are described using complex operators acting on the vacuum state which change the quantum numbers in a well-defined manner.
If we can isolate a compact spacelike region containing a set of field excitations, we can call those a particle. The individual field quanta which make up the particle can interact, however, as long as all conservation laws are obeyed. Hence the term "particle" is associated with an interacting system of field quanta isolated within a spacelike region of spacetime.
Quantum Gravity Concept Map Index:
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©1997, Kenneth R. Koehler. All Rights Reserved.