1 Introduction
1.1 High energy
1.2 Doubly special relativity
1.3 Newton–Hooke: de Sitter special relativity in the limit v ≪ c
1.

In | mathematical | physics, | de | Sitter | invariant | special | relativity | is | the | speculative | idea | that | the | fundamental | symmetry | group | of | spacetime | is | the | indefinite | orthogonal | group | SO(4,1), | that | of | de | Sitter | space. | In | the | standard | theory | of | general | relativity, | de | Sitter | space | is | a | highly | symmetrical | special | vacuum | solution, | which | requires | a | cosmological | constant | or | the | stress–energy | of | a | constant | scalar | field | to | sustain. | ||||||||||||||||||||||

The | idea | of | de | Sitter | invariant | relativity | is | to | require | that | the | laws | of | physics | are | not | fundamentally | invariant | under | the | Poincaré | group | of | special | relativity, | but | under | the | symmetry | group | of | de | Sitter | space | instead. | With | this | assumption, | empty | space | automatically | has | de | Sitter | symmetry, | and | what | would | normally | be | called | the | cosmological | constant | in | general | relativity | becomes | a | fundamental | dimensional | parameter | describing | the | symmetry | structure | of | spacetime. | |||||||||||||||

First | proposed | by | Luigi | Fantappiè | in | 1954, | the | theory | remained | obscure | until | it | was | rediscovered | in | 1968 | by | Henri | Bacry | and | Jean-Marc | Lévy-Leblond. | In | 1972, | Freeman | Dyson | popularized | it | as | a | hypothetical | road | by | which | mathematicians | could | have | guessed | part | of | the | structure | of | general | relativity | before | it | was | discovered.[1] | The | discovery | of | the | accelerating | expansion | of | the | universe | has | led | to | a | revival | of | interest | in | de | Sitter | invariant | theories, | in | conjunction | with | other | speculative | proposals | for | new | physics, | like | doubly | special | relativity. |

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1.

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