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A gauge symmetry of a Lagrangian is defined as a differential operator on some vector bundle taking its values in the linear space of (variational or exact) symmetries of . Therefore, a gauge symmetry of L {\displaystyle L} depends on sections of E {\displaystyle E} and their partial derivatives. [ 1 ]
Gauge theory in mathematics should not be confused with the closely related concept of a gauge theory in physics, which is a field theory which 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 ...
Quantum electrodynamics is an abelian gauge theory with the symmetry group U(1) and has one gauge field, the electromagnetic four-potential, with the photon being the gauge boson. The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3) and has a total of twelve gauge bosons: the photon , three weak bosons ...
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object
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.
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For example, the configuration space of a rigid body such as a satellite is the group of Euclidean motions (translations and rotations in space), while the configuration space for a liquid crystal is the group of diffeomorphisms coupled with an internal state (gauge symmetry or order parameter).
3. Truffle Oil – Martha Stewart. Truffle oil is your ingredient to make food instantly classy—or, more accurately, expensive. However, its rather pungent flavor isn’t for everyone, and it ...