nLab force




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



Physical bodies interact. The effects of binary interactions between point particles are known to be summarizable in vector quantities called forces applied to any body in an interaction; namely the forces on one body from each of several other bodies add up as vectors and such vector sum of forces on the body is proportional to the acceleration of the body (hence Newton's second law F=maF = m a is not a definition of force but a real law).

Thus force is a vector-like quantity which is a manifestation of the interaction between bodies. If body AA acts with force FF on body BB then BB acts on AA with the force F-F of the opposite vector value. These two forces do not cancel as they act on different bodies and at different points in space, though they are along the same line.

Sometimes one abstracts the forces on a system of bodies from the background by “potential energy” of the particles. Then the background acts on each particle with a force equal to the negative gradient of the potential energy.

In quantum field theory the forces appear mediated by particles which get exchanged between the bodies in interaction. For example, the strong nuclear force is mediated by gluons. There are 4 known fundamental forces in nature and all others are derived from them: the electromagnetic, weak, strong and gravitational force; and the first three are unified in the standard model of particle physics.

In nuclei there are also effective forces which are not of vector but of tensorial nature, and effective forces involving more than two bodies. But such quantum systems are far from classical mechanical systems.




Classification of long-range forces

Classification of possible long-range forces, hence of scattering processes of massless fields, by classification of suitably factorizing and decaying Poincaré-invariant S-matrices depending on particle spin, leading to uniqueness statements about Maxwell/photon-, Yang-Mills/gluon-, gravity/graviton- and supergravity/gravitino-interactions:


Last revised on December 18, 2019 at 11:27:03. See the history of this page for a list of all contributions to it.