invariance under group

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• Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

• Invariance mechanics — In physics, invariance mechanics, in its simplest form, is the rewriting of the laws of quantum field theory in terms of invariant quantities only. For example, the positions of a set of particles in a particular coordinate system is not… …   Wikipedia

• Scale invariance — In physics and mathematics, scale invariance is a feature of objects or laws that do not change if length scales (or energy scales) are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as… …   Wikipedia

• Modular invariance — In theoretical physics, modular invariance is the invariance under the group such as SL(2,Z) of large diffeomorphisms of the torus. The name comes from the classical name modular group of this group, as in modular form theory. In string theory,… …   Wikipedia

• Renormalization group — In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the… …   Wikipedia

• Poincaré group — In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime. It is a 10 dimensional noncompact Lie group. The abelian group of translations is a normal subgroup while the Lorentz… …   Wikipedia

• Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 …   Wikipedia

• Gauge theory — For a generally accessible and less technical introduction to the topic, see Introduction to gauge theory. In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations …   Wikipedia

• Introduction to gauge theory — This article is an accessible, non technical introduction to the subject. For the main encyclopedia article, see Gauge theory. Quantum field theory …   Wikipedia

• Symmetry in physics — refers to features of a physical system that exhibit the property of symmetry that is, under certain transformations, aspects of these systems are unchanged , according to a particular observation. A symmetry of a physical system is a physical or …   Wikipedia

• Invariant (mathematics) — In mathematics, an invariant is a property of a class of mathematical objects that remains unchanged when transformations of a certain type are applied to the objects. The particular class of objects and type of transformations are usually… …   Wikipedia