What is scalar field?

  • (noun): A field of scalars.

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:

Scalar Electrodynamics
... 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 ...
Scale Invariance in Quantum Field Theory - Massless 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 ...
Self-creation Cosmology - The New (2002) Theory
... 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 ...
Classical 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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