In physics, a field is an assignment of a quantity to every point in space. For example, one can speak of a gravitational field, which assigns a gravitational potential to each point in space. The isotherms shown in weather bulletins every day on TV are a picture of a temperature field on the surface of the earth. Fields are classified by space-time symmetries or by internal symmetries. The willingness to question previously held truths and search for new answers resulted in a period of major scientific advancements, now known as the Scientific Revolution. ... The gravitational field is a field that causes bodies with mass to attract each other. ... An isotherm is a line of equal or constant temperature on a graph, plot, or map; an isopleth of temperature. ...

Space-time symmetries

Fields are often classified by their behaviour under the symmetry transformations of space, ie, under rotations and translations. The terms used in this classification are — Symmetry is a characteristic of geometrical shapes, equations and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ... This article is about rotation as a movement of a physical body. ... Translation is an activity comprising the interpretation of the meaning of a text in one language—the source text—and the production of a new, equivalent text in another language—called the target text, or the translation. ...

• Scalar fields (such as temperature) whose values are given by a single variable at each point of space. This value does not change under transformations of space.
• vector fields (such as the magnitude and direction of the force at each point in a magnetic field) which are specified by attaching a vector to each point of space. The components of this vector transform between themselves as usual under rotations in space.
• tensor fields, (such as the stress tensor of a crystal) specified by a tensor at each point of space. The components of the tensor transform between themselves as usual under rotations in space.
• spinor fields are useful in quantum field theory.

In relativity a similar classification holds, except that scalars, vectors and tensors are defined with respect to the Poincare symmetry of spacetime. In mathematics and physics, a scalar field associates a single number (or scalar) to every point in space. ... Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in Euclidean space. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ... In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. ... Stress tensor In physics, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. ... In mathematics and physics, in particular in the theory of the orthogonal groups, spinors are certain kinds of mathematical objects (group representations of Spin(N), roughly speaking) similar to vectors, but which change sign under a rotation of radians. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... Luis is a Feizos love child. ... Poincare symmetry is the full symmetry of special relativity and includes translations (ie, displacements) in time and space (these form the Abelian Lie group of translations on space-time) rotations in space (this forms the non-Abelian Lie group of 3-dimensional rotations) boosts, ie, transformations connecting two uniformly moving...

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...φ_N). For example, in weather prediction these may be temperature, pressure, humidity, etc.

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 fields as scalars, vectors or tensors under internal symmetries.

Classical and quantum fields

Michael Faraday first realized the importance of a field as a physical object, during his investigations into magnetism. He realized that electric and magnetic fields are not only as fields of force which dictate the motion of particles, but also have independent physical reality because they carry energy. Michael Faraday Michael Faraday (September 22, 1791 – August 25, 1867) was a British scientist (a physicist and chemist) who contributed significantly to the fields of electromagnetism and electrochemistry. ... In physics, magnetism is a phenomenon by which materials exert an attractive or repulsive force on other materials. ... In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ...

These ideas eventually led to the creation by James Clerk Maxwell of the first unified field theory in physics with the introduction of equations (in the 19th century) for the electromagnetic field. The modern version of these equations are called Maxwell's equations. At the end of the 19th century, the electromagnetic field was understood as a collection of two vector fields in space. Nowadays, one recognizes this as a single (rank 2) tensor field in spacetime. James Clerk Maxwell James Clerk Maxwell (June 13, 1831 - November 5, 1879) was a Scottish physicist, born in Edinburgh. ... An electromagnetic field is composed of two related vectorial fields, the electric field and the magnetic field. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... An electromagnetic field is composed of two related vectorial fields, the electric field and the magnetic field. ...

Einstein's theory of gravity, called general relativity is another example of a field theory. It involves a (rank 4) tensor field in spacetime. Two-dimensional visualisation of space-time distortion. ...

One recognizes now that the universe is essentially quantum mechanical. So any field theory of real phenomena must be at base a quantum field theory. The quantum field theory arising from Maxwell's equations is called quantum electrodynamics. Nowadays one recognizes two more fundamental field theories of particle physics — quantum chromodynamics and electroweak theory. These three interactions are unified into the standard model of particle physics. General relativity has not yet been successfully quantized. Fig. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Quantum electrodynamics (QED) is a quantum field theory of electromagnetism. ... Quantum chromodynamics (QCD) is the physical theory describing one of the fundamental forces, the strong interaction. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... Particles explode from the collision point of two relativistic velocity (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Two-dimensional visualisation of space-time distortion. ...

There remain many areas in which classical field theory is useful, since the quantum nature of the universe may not manifest itself in every situation. Elasticity of materials, fluid dynamics and Maxwell's equations are some of many useful classical field theories. Some of them remain active areas of research. Elasticity has meanings in two different fields: In physics and mechanical engineering, the theory of elasticity describes how a solid object moves and deforms in response to external stress. ... This article or section should be merged with Fluid mechanics Fluid dynamics is the study of fluids (liquids and gases) in motion, and the effect of the fluid motion on fluid boundaries, such as solid containers or other fluids. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

See also

• Quantum field theory and gauge theory
• Electromagnetic field and Maxwell's equations
• General relativity and the standard model of particle physics
• Elasticity and fluid dynamics

Quantum field theory (QFT) is the application of quantum mechanics to fields. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... An electromagnetic field is composed of two related vectorial fields, the electric field and the magnetic field. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Two-dimensional visualisation of space-time distortion. ... This is a detailed description of the standard model (SM) of particle physics. ... Particles explode from the collision point of two relativistic velocity (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Elasticity has meanings in two different fields: In physics and mechanical engineering, the theory of elasticity describes how a solid object moves and deforms in response to external stress. ... This article or section should be merged with Fluid mechanics Fluid dynamics is the study of fluids (liquids and gases) in motion, and the effect of the fluid motion on fluid boundaries, such as solid containers or other fluids. ...