Vacuum fluctuations of a scalar field in a rectangular waveguide

✍ Scribed by R.B. Rodrigues; N.F. Svaiter

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 271 KB
• Volume: 328
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(03)00575-2

✦ Synopsis

An analysis of one-loop vacuum uctuations associated with a scalar ÿeld conÿned in the interior of a inÿnite waveguide of rectangular cross section is presented. We ÿrst consider the massless scalar ÿeld deÿned in a four-dimensional Euclidean space. To identify the divergences of the vacuum uctuations we use a combination of dimensional and zeta function analytic regularization procedures. The divergences which occur in the one-loop vacuum uctuations fall into two distinct classes: local ones that are renormalized by the introduction of the usual bulk counterterms, and surface and edge divergences that demand counterterms concentrated on the boundaries. We present the detailed form of the surface and edge divergences. Finally we discuss how to generalize our calculations for a conÿned massive scalar ÿeld deÿned in a higher dimensional Euclidean space.