On the Birman-Schwinger principle applied to −Δ+m2−m

The Birman-schwinger Principle on the Essential Spectrum

Let H0 and H be self-adjoint operators in a Hilbert space. We consider the spectral projections of H0 and H corresponding to a semi-infinite interval of the real line. We discuss the index of this pair of spectral projections and prove an identity which extends the Birman-Schwinger principle onto the essential spectrum. We also relate this index to the spectrum of the scattering matrix for the ...

The Birman-schwinger Principle in Von Neumann Algebras of Finite Type

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the a...

on the status of mixed methods research in applied linguistics

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The Schwinger Action Principle and Its Applications to Quantum Mechanics

Infrared Behaviour, Sources and the Schwinger Action Principle

An action principle technique is used to examine the infra-red problem in the effective action for gauge field theories. It is shown by means of a dynamical analogy that the renormalization group and the ansatz of non-local sources can be simultaneously understood through generalized variations of an action supplemented by sources in the manner of the Schwinger action principle. It is shown tha...