Casimir effect in polymer scalar field theory

• Published in: arXiv.org
• Main Authors: Escobar, C A, Chan-López, E, Martín-Ruiz, A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 29.01.2020
• Subjects: Energy spectra; Field theory; Mathematical analysis; Physics - High Energy Physics - Phenomenology; Plates; Polymers; Quantum theory; Scalars; Yang-Mills theory; Zero point energy
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2001.11059

In this paper, we study the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance \(L\), due to the presence of a minimal length \(\lambda\) arising from a background independent (polymer) quantization scheme. To this end, we polymer-quantize the classical Klein-Gordon Hamiltonian for a massive scalar field confined between the plates and obtain the energy spectrum. The minimal length scale of the theory introduces a natural cutoff for the momenta in the plane parallel to the plates and a maximum number of discrete modes between the plates. The zero-point energy is calculated by summing over the modes, and by assuming \(\lambda \ll L\), we expressed it as an expansion in powers of \(1/N\), being \(N=L/ \lambda\) the number of points between the plates. Closed analytical expressions are obtained for the Casimir energy in the cases of small and large scalar mass limits.