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Representation theory of the Lorentz group

The Lorentz group is a Lie group of symmetries of the spacetime of special relativity. This group can be realized as a collection of matrices, linear transformations, or unitary operators on some Hilbert space; it has a variety of representations. This group is significant because special relativity together with quantum mechanics are the two physical…

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Overview

Finite-dimensional representations

History

Action on function spaces

Infinite-dimensional unitary representations

Explicit formulas

Physics applications

Open problems

Freely available online references

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Representation theory of the Lorentz group

Nodes246
Edges245
Triples32
Avg. degree1.99
Density0.00813
Components1

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Representation theory of the Lorentz group

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related to history · 20
Representation theory of the Lorentz group → By, Cartan, Clifford, Dirac, Eugene Wigner, Harish-Chandra, History, In, Lie, Lorentz, Lorentz Lie, Mathematicians Hermann Weyl, Physicist Paul Dirac, Richard Brauer, Sophus Lie, The, The Lorentz, Valentine Bargmann, Weyl-Brauer, Wilhelm Killing
related to Open problems · 6
Representation theory of the Lorentz group → Even, Lorentz, Poincaré, Tachyons, The, This

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Important terminology

group displaystyle representations representation mathbb lorentz lie irreducible sl mathfrak algebra text theory unitary isbn space spin left end right

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SubjectPredicateObjectConfidenceSrc
QED which is invariant under space parityinstance ofis then antiunitary rather than a complex-linear representation operator.When constructing theories0.80text
time reversalinstance ofis then antiunitary rather than a complex-linear representation operator.When constructing theories0.80text
Dirac spinors may be usedinstance ofis then antiunitary rather than a complex-linear representation operator.When constructing theories0.80text
while theories that do notinstance ofis then antiunitary rather than a complex-linear representation operator.When constructing theories0.80text
such as the electroweak forceinstance ofis then antiunitary rather than a complex-linear representation operator.When constructing theories0.80text
must be formulated in terms of Weyl spinorsinstance ofis then antiunitary rather than a complex-linear representation operator.When constructing theories0.80text
Representation theory of the Lorentz grouprelated to historyThe0.60section
Representation theory of the Lorentz grouprelated to historyLorentz0.60section
Representation theory of the Lorentz grouprelated to historyLie0.60section
Representation theory of the Lorentz grouprelated to historySophus Lie0.60section
Representation theory of the Lorentz grouprelated to historyBy0.60section
Representation theory of the Lorentz grouprelated to historyWilhelm Killing0.60section

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