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Temperature Dependence of the CP N‐1 Model and the Analogy with Quantum Chromodynamics
Author(s) -
Actor Alfred
Publication year - 1985
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190330604
Subject(s) - quantum chromodynamics , physics , quantization (signal processing) , conformal map , charge (physics) , quantum field theory , analogy , thermal quantum field theory , conformal field theory , euclidean geometry , mathematical physics , quantum electrodynamics , quantum mechanics , quantum , quantum gravity , geometry , mathematics , algorithm , linguistics , philosophy
The two‐dimensional CP N ‐1 model — a simple field‐theoretic analogue of four‐dimensional quantum chromodynamics (QCD) — is analysed and reviewed. The major themes are the temperature dependence of the CP N ‐1 model, and the analogy between CP N ‐1 and QCD. A detailed treatment of the 1/ N approximation of the CP N ‐1 model is given. The main results emerging from this approximation are discussed at length. These are: asymptotic freedom, dimensional transmutation, confinement and topological charge nonquantization at zero temperature T = O, screening and topological charge quantization at finite temperature T . The analogy with QCD is explained in detail. A new, qualitative, analysis of the CP N ‐1 model at finite temperature is introduced. This approach exploits the conformal invariance of the model to “heat” an arbitrary CP N ‐1 field from T = O to finite temperature. This is achieved by conformal‐transforming the flat Euclidean space‐time of the T = O theory to the cylindrical space‐time of the finite temperature theory.