An important example of this is the inhomogeneous Lorentz group.

This is due to the non-compactness of the Lorentz group.

It corresponds to the representation of the Lorentz group, or rather, its part.

Such a circle corresponds to the space rotation parameters of the Lorentz group.

Language and terminology is used as in Representation theory of the Lorentz group.

A canonical reference; see chapters 1-6 for representations of the Lorentz group.

As usual, one introduces a connection field that allows us to gauge the Lorentz group.

The Lorentz group of special relativity has a variety of representations.

This is one way to understand why the restricted Lorentz group is six dimensional.

However, there are of course spinorial representations of the Lorentz group.

The restricted Lorentz group arises in other ways in pure mathematics.

The restricted Lorentz group has often been presented through a facility of biquaternion algebra.

It is the restricted Lorentz group of three-dimensional Minkowski space.

The Lie algebra of the Lorentz group is expressed by bivectors.

One often says that the restricted Lorentz group and the rotation group are doubly connected.

The Lorentz group are the transformations that keep the origin fixed, but translations are not included.

An excellent reference on Minkowski spacetime and the Lorentz group.

Meanwhile, the Lorentz group generators enjoy their usual relations among themselves but act non-linearly on the momentum space.

In many special cases, for example for complex semisimple group or the Lorentz groups, there are simple methods to develop the theory directly.

The term particle is used to label the irreducible representations of the Lorentz group that are permitted by the field.

Technically these are really representations of the double cover of the Lorentz group called a spin group.

Its rotation group is the Lorentz group.

Since the Lorentz group of special relativity is not compact, will not be unitary, so .

While there is only one vector representation for each Lorentz group, in general there are several different spinorial representations.

Following is an overview of the Lorentz group; a treatment of boosts and rotations in spacetime.