Instanton solutions on the polymer harmonic oscillator. (18th May 2017)

• Record Type: Journal Article
• Authors: Austrich-Olivares, Joan A; Garcia-Chung, Angel; David Vergara, J
• Is Part Of: Classical and quantum gravity. Volume 34:Number 11(2017:Jun.)
• Publication Date: 2017-05-18
• Subjects: polymer harmonic oscillator -- instanton methods -- polymer spectrum; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/aa6d88
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: We have computed, using instanton methods, the first allowed energy band for the polymer harmonic oscillator. The eigenvalues within the band are labelled by a discrete parameter λ which results from the non-separability of the polymer Hilbert space. It is shown throughout the article the role played by λ in the full quantization of the polymer harmonic oscillator. The result is consistent with the band structure of the standard quantum pendulum but with pure point spectrum. Consequently, an effective infinite degeneracy emerges in the formal limit μ / l 0 → 0 where l 0 is the characteristic length of the vacuum eigenfunction of a quantum harmonic oscillator.