RESEARCH ON PHYSICS REPORTED BY SCIENTISTS AT YEREVAN STATE UNIVERSITY

Science Letter
November 24, 2009

"By using the generalized Abel-Plana formula, we derive a summation
formula for the series over the zeros of a combination of the
associated Legendre functions with respect to the degree. The
summation formula for the series over the zeros of the combination
of the Bessel functions, previously discussed in the literature, is
obtained as a limiting case," researchers in Yerevan, Armenia report
(see also Physics).

"As an application we evaluate the Wightman function for a scalar
field with a general curvature coupling parameter in the region
between concentric spherical shells on a background of constant
negative curvature space. For the Dirichlet boundary conditions the
corresponding mode-sum contains the series over the zeros of the
combination of the associated Legendre functions. The application of
the summation formula allows us to present the Wightman function in
the form of the sum of two integrals. The first one corresponds to the
Wightman function for the geometry of a single spherical shell and
the second one is induced by the presence of the second shell. The
boundary-induced part in the vacuum expectation value of the field
squared is investigated," wrote A.A. Saharian and colleagues, Yerevan
State University.

The researchers concluded: "For points away from the boundaries the
corresponding renormalization procedure is reduced to that for the
boundary-free part."

Saharian and colleagues published their study in the Journal of Physics
a – Mathematical and Theoretical (A summation formula over the zeros
of a combination of the associated Legendre functions with a physical
application. Journal of Physics a – Mathematical and Theoretical,
2009;42(46):65210).

For additional information, contact A.A. Saharian, Yerevan State
University, Dept. of Physics, 1 Alex Manoogian St., Yerevan 0025,
Armenia.

Publisher contact information for the Journal of Physics a –
Mathematical and Theoretical is: IOP Publishing Ltd., Dirac House,
Temple Back, Bristol BS1 6BE, England.