In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A field which is invariant under any Lorentz transformation is called a "scalar", in contrast to a vector or tensor field. The quanta of the quantized scalar field are spin-zero particles, and as such are bosons.
No fundamental scalar fields have been observed in nature, though the Higgs boson may yet prove the first example. However, scalar fields appear in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a "pseudoscalar", which means it is not invariant under parity transformations which invert the spatial directions, distinguishing it from a true scalar, which is parity-invariant. Because of the relative simplicity of the mathematics involved, scalar fields are often the first field introduced to a student of classical or quantum field theory.
In this article, the repeated index notation indicates the Einstein summation convention for summation over repeated indices. The theories described are defined in flat, D-dimensional Minkowski space, with (D-1) spatial dimension and one time dimension and are, by construction, relativistically covariant. The Minkowski space metric, has a particularly simple form: it is diagonal, and here we use the + − − − sign convention.
Read more about Scalar Field Theory: Quantum Scalar Field Theory, See Also
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