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  2. Gauge theory - Wikipedia

    en.wikipedia.org/wiki/Gauge_theory

    The "gauge covariant" version of a gauge theory accounts for this effect by introducing a gauge field (in mathematical language, an Ehresmann connection) and formulating all rates of change in terms of the covariant derivative with respect to this connection. The gauge field becomes an essential part of the description of a mathematical ...

  3. Introduction to gauge theory - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_gauge_theory

    A gauge theory is a type of theory in physics.The word gauge means a measurement, a thickness, an in-between distance (as in railroad tracks), or a resulting number of units per certain parameter (a number of loops in an inch of fabric or a number of lead balls in a pound of ammunition). [1]

  4. Gauge theory (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Gauge_theory_(mathematics)

    Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theory that admits gauge symmetry. In mathematics theory means a mathematical theory , encapsulating the general study of a collection of concepts or phenomena, whereas in the physical sense a gauge theory is a ...

  5. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    This mirrors the historical evolution of quantum field theory, since the electron component ψ e (describing the electron and its antiparticle the positron) is then the original ψ field of quantum electrodynamics, which was later accompanied by ψ μ and ψ τ fields for the muon and tauon respectively (and their antiparticles).

  6. Gauge covariant derivative - Wikipedia

    en.wikipedia.org/wiki/Gauge_covariant_derivative

    Consider a generic (possibly non-Abelian) gauge transformation acting on a component field = =.The main examples in field theory have a compact gauge group and we write the symmetry operator as () = where () is an element of the Lie algebra associated with the Lie group of symmetry transformations, and can be expressed in terms of the hermitian generators of the Lie algebra (i.e. up to a ...

  7. Topological Yang–Mills theory - Wikipedia

    en.wikipedia.org/wiki/Topological_Yang–Mills...

    In gauge theory, topological Yang–Mills theory, also known as the theta term or -term is a gauge-invariant term which can be added to the action for four-dimensional field theories, first introduced by Edward Witten. [1]

  8. Gauge symmetry (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Gauge_symmetry_(mathematics)

    Therefore, a gauge symmetry of depends on sections of and their partial derivatives. [1] For instance, this is the case of gauge symmetries in classical field theory. [2] Yang–Mills gauge theory and gauge gravitation theory exemplify classical field theories with gauge symmetries. [3]

  9. Supersymmetric gauge theory - Wikipedia

    en.wikipedia.org/wiki/Supersymmetric_gauge_theory

    A gauge theory is a field theory with gauge symmetry. Roughly, there are two types of symmetries, global and local. A global symmetry is a symmetry applied uniformly (in some sense) to each point of a manifold. A local symmetry is a symmetry which is position dependent.