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In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. [1] The only fundamental scalar quantum field that has been observed in nature is the Higgs field.
A scalar field such as temperature or pressure, where intensity of the field is represented by different hues of colors. In mathematics and physics, a scalar field is a function associating a single number to each point in a region of space – possibly physical space.
Standard Model of Particle Physics. The diagram shows the elementary particles of the Standard Model (the Higgs boson , the three generations of quarks and leptons , and the gauge bosons ), including their names, masses, spins, charges, chiralities, and interactions with the strong , weak and electromagnetic forces.
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x component for the x axis) of a vector wave without sources of waves ...
According to the definition of the gradient of a scalar function f, () = (), thus we have found a scalar-valued function f whose gradient is the path-independent vector field F (i.e., F is a conservative vector field.), as desired. [3]
As long as new physics appears below or around 10 14 GeV, the neutrino masses can be of the right order of magnitude. Theoretical and experimental research has attempted to extend the Standard Model into a unified field theory or a theory of everything , a complete theory explaining all physical phenomena including constants.
The scalar field, φ(x, t) is a function of a set of spatial variables, x, and a time variable, t. Consider first the linear theory. Like the electromagnetic field equations above, the equation of motion for this theory is also a wave equation,