On the renormalization in singular background fields

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On the renormalization in singular background
fields
M. Bordag, (University of Leipzig)

• Plan
• Motivation
• Vacuum energy and divergences
• Background fields becoming singular
• Plasma shell model
• Renormalization and finite vacuum energy

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Motivation

• general interest in Casimir effect, both,
  theoretical and experimental
• actual interest in connection with applications
  in nanotechnology
• New Research Networking Programme

New Trends and Applications of the Casimir Effect
(CASIMIR) Steering Committee Chair Dr.Astrid
Lambrecht (for details see webpage)
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Motivation divergences in the vacuum energy
Zero point (vacuum) energy
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Separation of divergences
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Resume from the previous discussion
smooth background fields -standard
renormalization procedure known from qft

• boundary conditions
• finite forces between disjunct bodies
• finite energy (cond. sphere, dilute ball)
• divergences left (diel. ball)

additional problem Singular background fields
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• in this way, the standard scheme does not work
• this was mentioned, e.g., in Graham, Jaffe, et
  al, Nucl.Phys, 677 (2004) 379,
• who came to the conclusion that the divergences
  in the sharp limit persist
• Here, Ill present a model which
• - has a singular background field (delta
  potential)
• - has a physically meaningful interpretation
  (c60)
• can be renormalized in the standard way
• has as a limiting case the conducting sphere

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Comments There is a coefficient for ½ The
coefficient for 3/2 is independent on Omega
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With these coefficients the renormalization can
be carried out There are contributions growing
with Omega
These can be included into the renormalization
like the divergent ones
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Conclusions We have constructed a model where
the ultraviolet divergences can be hidden in a
redefinition of the parameters of the classical
part The arbitrariness inherent to the
renormalization procedure is removed by
demanding the vacuum energy to take its correct
value for a conducting sphere Considered from
the point of view of a conducting sphere we have
a kind of physical regularization by making the
sphere semitransparent