Inverse Problems in Quantum Scattering Theory

We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We fix ambiguities in the renormalization by considering the asymptotic expansion of the vacuum energy as the mass gap tends to infinity (while keeping scattering data fixed) and dropping all terms proportional to non-negative powers or the logarithm of this mass gap. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and apply standard heat kernel subtractions with modifications which take the boundaries into account. Finally we discuss to what extent these procedures are equivalent to the usual renormalization condition that tadpoles vanish.

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“…For any reflectionless potential the phase shift can be represented as a sum over the bound states [23] …”

Section: Discussionmentioning

confidence: 99%

“…All necessary information on one-dimensional scattering theory can be found in [23]. Consider a reflectionless potential V (x) localized around the point x = 0 (and vanishing for x → ±∞).…”

mentioning

confidence: 99%

Heat kernels and zeta-function regularization for the mass of the supersymmetric kink

et al. 2002

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“…It is well investigated, please refer to the textbook [64] for example. We note the following properties.…”

Section: Background Depending On One Cartesian Coordinatementioning

confidence: 99%

New developments in the Casimir effect

2001

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We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a direct manifestation of the boundary dependence of quantum vacuum. We discuss in depth the general structure of the infinities in the field theory which are removed by a combination of zeta-functional regularization and heat kernel expansion. Different representations for the regularized vacuum energy are given. The Casimir energies and forces in a number of configurations of interest to applications are calculated. We stress the development of the Casimir force for real media including effects of nonzero temperature, finite conductivity of the boundary metal and surface roughness. Also the combined effect of these important factors is investigated in detail on the basis of condensed matter physics and quantum field theory at nonzero temperature. The experiments on measuring the Casimir force are also reviewed, starting first with the older measurements and finishing with a detailed presentation of modern precision experiments. The latter are accurately compared with the theoretical results for real media. At the end of the review we provide the most recent constraints on the corrections to Newtonian gravitational law and other hypothetical long-range interactions at submillimeter range obtained from the Casimir force measurements.

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“…We now recall the well known W.S.K. (Whittaker-Shannon-KotePnikov) sampling Theorem ( [8] and [15] where B 6 (n) = y s (n, n 2 ). depending on the sign of B' NS .…”

Section: Samplingmentioning

confidence: 99%