Scalar field theory

A field theory whose fundamental field assigns a single scalar value to each point in space-time. Its models describe how that field varies and interacts with matter and other fields.

Scalar field: A quantity assigning one number to every point in space-time. It is the basic dynamical object whose values the theory describes.
Klein–Gordon equation: A relativistic wave equation for a free scalar field. It describes propagation when the scalar field has a quadratic mass term.
Higgs field: The scalar field whose nonzero vacuum value gives mass to elementary particles through electroweak interactions. It is the experimentally established scalar field of the Standard Model.
Vector field theory: A field theory whose fundamental field assigns a vector to each space-time point. Vector fields carry directional components absent from a scalar field.
Lagrangian density: A function of fields and their derivatives whose space-time integral defines an action. Scalar theories specify dynamics through a Lagrangian density built from the field.
Scalar potential: A function of a scalar field that contributes to its energy and dynamics. Its shape controls masses, self-interactions, and possible vacuum states.
Higgs mechanism: A mechanism by which gauge bosons acquire mass through interactions with a scalar field. The Higgs field realizes this mechanism in electroweak theory.
Tensor field theory: A field theory whose fundamental fields assign tensors to points in space-time. Tensor fields encode multiple components and transformation rules beyond scalar values.
Euler–Lagrange equation: A differential equation obtained by making an action stationary under variations of its fields. Varying the scalar-field action yields its equation of motion.
Spontaneous symmetry breaking: A state of a system fails to share a symmetry of its governing laws. A scalar potential can favor a vacuum that breaks the theory's symmetry.

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Gauge theoryCompared with: A simple scalar theory can lack the connection fields that characterize gauge dynamics.