In physics, a field is an assignment of a physical quantity to every point in space (or, more generally, spacetime). A field is thus viewed as extending throughout a large region of space so that its influence is all-pervading. The strength of a field usually varies over a region.
Fields are usually represented mathematically by scalar, vector and tensor fields. For example, one can model a gravitational field by a vector field where a vector indicates the force a unit mass would experience at each point in space. Other examples are temperature fields or air pressure fields, which are often illustrated on weather reports by isotherms and isobars by joining up the points of equal temperature or pressure respectively.
Symmetries of fields
A convenient way of classifying fields (classical or quantum) is by the symmetries it possesses. Physical symmetries are usually of two types:
Internal symmetries
Fields may have internal symmetries in addition to spacetime symmetries. For example, in many situations one needs fields which are a list of space-time scalars: (φ1,φ2...φN). For example, in weather prediction these may be temperature, pressure, humidity, etc. In particle physics, the color symmetry of the interaction of quarks is an example of an internal symmetry of the strong interaction, as is the isospin or flavour symmetry.
If there is a symmetry of the problem, not involving spacetime, under which these components transform into each other, then this set of symmetries is called an internal symmetry. One may also make a classification of the charges of the fields under internal symmetries.
See also
References
- Landau, Lev D. and Lifshitz, Evgeny M. (1971). Classical Theory of Fields (3rd ed.). London: Pergamon. ISBN 0-08-016019-0. Vol. 2 of the Course of Theoretical Physics.