Particle (physics)

A particle is an entity described as a localized constituent in an appropriate physical model. In classical mechanics, a point particle has a position and trajectory while its internal size is neglected. This approximation can describe an extended object when the omitted structure does not affect the question being studied.

In quantum mechanics, a quantum particle has a state described by a wave function or a more general state description, with probabilistic measurement outcomes. Quantum field theory describes particle states as excitations of fields. A proton can be treated as a particle in one experiment while its quark and gluon structure matters in another. The particle description therefore specifies what is being resolved, rather than asserting that every particle is a structureless classical point.

A point particle is an idealization whose position is represented by a single spatial point and whose internal size and structure are omitted. It can still carry parameters such as mass, electric charge or spin.

The approximation is useful when the relevant length scales are much larger than the object's size and internal deformation is unimportant. A planet can be treated as a point mass for some orbital calculations even though it is extended. Short-distance fields and self-interaction can expose the limits of the idealization.

A scalar particle has zero intrinsic spin. A scalar-field excitation provides its relativistic description. Spin zero alone does not force its decay matrix element to be independent of internal invariant masses; resonance dynamics can still produce a nonuniform three-body distribution.

A particle with zero invariant rest mass. A positive-energy massless state has $E=|\mathbf{p}|$ in natural units and has no rest frame. Its finite-helicity representations differ from massive spin representations.

A particle with strictly positive rest mass. Its relativistic energy obeys $E^2=p^2{c}^2+m^2{c}^4$, and its speed in an inertial frame is below the speed of light.

A particle with zero net electric charge.

A particle number counts the particles of a specified kind in a system. For a fixed collection, $N$ is a nonnegative integer. In a variable-number quantum system, distinguish a measured particle number, the particle number operator, and its expected value.

The rate at which particles cross an oriented surface, measured as particle count per unit time. If a local continuity equation has number density $n$ and current density ${\mathbf{j}}_N$, then ${\partial }_{t}n+\nabla \cdot {\mathbf{j}}_N=0$ and $J_N={\int }_S{\mathbf{j}}_N\cdot d\mathbf{S}$. In a closed two-reservoir system, a left-to-right particle current is $-d{N}_L/dt=d{N}_R/dt$. Neutral particles carry this current without an associated electric current.