## Scalar Field

In mathematics and physics, a **scalar field** associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime). Examples used in physics include the temperature distribution throughout space, the pressure distribution in a fluid, and spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar field theory

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### Some articles on scalar field:

... In theoretical physics,

**scalar**electrodynamics is a theory of a U(1) gauge

**field**coupled to a charged spin 0

**scalar field**that takes the place of the Dirac fermions in "ordinary" quantum electrodynamics ... The

**scalar field**is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the Abelian Higgs mechanism ... The model consists of a complex

**scalar field**minimally coupled to a gauge

**field**...

**Scalar Field**Theory

... Free, massless quantized

**scalar field**theory has no coupling parameters ... is not scale-invariant, there do exist scale-invariant quantized

**scalar field**theories other than the Gaussian fixed point ...

... that mass is created out of gravitational and

**scalar fields**in accordance with the Principle of Mutual Interaction (PMI) ... The

**scalar field**is a source for the matter-energy

**field**if and only if the matter-energy

**field**is a source for the

**scalar field**." As the source for the

**scalar field**is the trace of the stress-energ ... conservation of energy requires the energy expended in lifting an object against a gravitational

**field**to be translated into an increase in its rest mass ...

**Scalar Field**- Other Kinds of Fields

... Vector

**fields**, which associate a vector to every point in space ... Some examples of vector

**fields**include the electromagnetic

**field**and the Newtonian gravitational

**field**... Tensor

**fields**, which associate a tensor to every point in space ...

**Scalar Field**Theory - Complex

**Scalar Field**Theory

... In a complex

**scalar field**theory, the

**scalar field**takes values in the complex numbers, rather than the real numbers ... form This has a U(1) symmetry, whose action on the space of

**fields**rotates, for some real phase angle ... As for the real

**scalar field**, spontaneous symmetry breaking is found if m2 is negative ...

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—Mary Church Terrell (1863–1954)