Canonical quantization of a massive particle on AdS3

James Lucietti*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The classical theory for a massive free particle moving on the group manifold AdS3 = SL(2, ℝ) is analysed in detail. In particular a symplectic structure and two different sets of canonical coordinates are explicitly found, corresponding to the Cartan and Iwasawa decomposition of the group. Canonical quantization is performed in two different ways; by imposing the future-directed constraint before and after quantization. It is found that this leads to different quantum theories. The Hilbert space of either theory decomposes into the sum of certain irreducible representations of sl(2, ℝ) ⊕ sl(2, ℝ); however, depending on how the constraint is imposed we get different representations. Quantization of the mass occurs, although a continuum exists in the unconstrained theory corresponding to particles that can reverse their direction in time. A quantization in terms of the "chiral" variables of the theory is also carried out giving the same results. Comparisons are made between QFT in AdS3 and the quantum mechanics derived, and it is found that one of the quantum theories is consistent with the Breitenlohner-Freedman bound.

Original languageEnglish
Pages (from-to)345-361
Number of pages17
JournalJournal of High Energy Physics
Volume7
Issue number5
DOIs
Publication statusPublished - 1 May 2003

Keywords

  • Conformal Field Models in String Theory
  • Field Theories in Lower Dimensions
  • Integrable Field Theories
  • Sigma Models

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