# Lorentz Group

In physics (and mathematics), the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical setting for all (nongravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz.

The mathematical form of

• the kinematical laws of special relativity,
• Maxwell's field equations in the theory of electromagnetism,
• Dirac's equation in the theory of the electron,

are each invariant under the Lorentz transformations. Therefore the Lorentz group is said to express the fundamental symmetry of many of the known fundamental Laws of Nature.

### Other articles related to "lorentz group, group, lorentz":

Higher-dimensional Supergravity - Counting Gravitinos
... representation and the vector representation of the Lorentz group ... is only one vector representation for each Lorentz group, in general there are several different spinorial representations ... Technically these are really representations of the double cover of the Lorentz group called a spin group ...
Lorentz Group - General Dimensions
... The concept of the Lorentz group has a natural generalization to any spacetime dimension ... Mathematically, the Lorentz group of n+1 dimensional Minkowski space is the group O(n,1) (or O(1,n)) of linear transformations of Rn+1 which preserve the quadratic form Many of the properties ... For instance, the Lorentz group O(n,1) has four connected components, and it acts by conformal transformations on the celestial (n−1)-sphere in n+1 dimensional Minkowski space ...
Non-critical String Theory: Lorentz Invariance
... a universal method to maintain explicit Lorentz invariance in any quantum relativistic theory ... Lorentz transformations change the position of the world sheet with respect to these fixed planes, and they are followed by reparametrizations of the world sheet ... the quantum level the reparametrization group has anomaly, which appears also in Lorentz group and violates Lorentz invariance of the theory ...
Lorentz Invariance In Loop Quantum Gravity
... As such, it can be argued that LQG respects local Lorentz invariance ... Global Lorentz invariance is broken in LQG just like it is broken in general relativity (unless one is dealing with Minkowski spacetime, which is one particular ... possible local and global violations of Lorentz invariance beyond those expected in straightforward general relativity ...
Derivation of A Bispinor Representation - Introduction
... elements of a particular representation space of the (½,0)⊕ (0,½) representation of the Lorentz group ... Language and terminology is used as in Representation theory of the Lorentz group ... A representation of the Lie algebra so(31) of the Lorentz group O(31) will emerge among matrices that will be chosen as a basis (as a vector space) of the ...

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