{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:56:25Z","timestamp":1753872985426,"version":"3.41.2"},"reference-count":12,"publisher":"AIP Publishing","issue":"7","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2011,7,1]]},"abstract":"<jats:p>We examine the mathematical and physical significance of the spectral density \u03c3(\u03c9) introduced by Ford [Phys. Rev. D\u200838, 528 (1988)]10.1103\/PhysRevD.38.528, defining the contribution of each frequency to the renormalised energy density of a quantum field. Firstly, by considering a simple example, we argue that \u03c3(\u03c9) is well defined, in the sense of being regulator independent, despite an apparently regulator dependent definition. We then suggest that \u03c3(\u03c9) is a spectral distribution, rather than a function, which only produces physically meaningful results when integrated over a sufficiently large range of frequencies and with a high energy smooth enough regulator. Moreover, \u03c3(\u03c9) is seen to be simply the difference between the bare spectral density and the spectral density of the reference background. This interpretation yields a simple \u201crule of thumb\u201d to writing down a (formal) expression for \u03c3(\u03c9) as shown in an explicit example. Finally, by considering an example in which the sign of the Casimir force varies, we show that the spectrum carries no manifest information about this sign; it can only be inferred by integrating \u03c3(\u03c9).<\/jats:p>","DOI":"10.1063\/1.3614003","type":"journal-article","created":{"date-parts":[[2011,7,25]],"date-time":"2011-07-25T22:33:07Z","timestamp":1311633187000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["The Casimir spectrum revisited"],"prefix":"10.1063","volume":"52","author":[{"given":"Carlos A. R.","family":"Herdeiro","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica da Universidade de Aveiro 1 , Campus de Santiago, 3810-183 Aveiro, Portugal"},{"name":"Faculdade de Ci\u00eancias da Universidade do Porto \u2014 FCUP 2 Centro de F\u00edsica do Porto \u2014 CFP, Departamento de F\u00edsica e Astronomia, , Rua do Campo Alegre, 4169-007 Porto, Portugal"}]},{"given":"Marco O. P.","family":"Sampaio","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias da Universidade do Porto \u2014 FCUP 2 Centro de F\u00edsica do Porto \u2014 CFP, Departamento de F\u00edsica e Astronomia, , Rua do Campo Alegre, 4169-007 Porto, Portugal"}]},{"given":"Jaime E.","family":"Santos","sequence":"additional","affiliation":[{"name":"Faculdade de Ci\u00eancias da Universidade do Porto \u2014 FCUP 2 Centro de F\u00edsica do Porto \u2014 CFP, Departamento de F\u00edsica e Astronomia, , Rua do Campo Alegre, 4169-007 Porto, Portugal"},{"name":"Max Planck Institute for the Physics of Complex Systems 3 , Noethnitzer Str. 38, D-01187 Dresden, Germany"}]}],"member":"317","published-online":{"date-parts":[[2011,7,25]]},"reference":[{"key":"2023062804091095100_c1","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1103\/PhysRevD.38.528","volume":"38","year":"1988","journal-title":"Phys. Rev. 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