The generalized Birman-Schwinger principle

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...

Generalized Rarita-Schwinger Equations

The Rarita-Schwinger equations are generalised for the delta baryon having spin 3/2 and isospin 3/2. The coupling of the nucleon and the delta fields is studied. A possible generalisation of the Walecka model is proposed.

Generalized Schwinger Mass Formula

We generalize Schwinger’s original mass formula to the case of an additional isosinglet which mixes with the nonet mesons, by considering the corresponding 3×3 mass matrix in the most general case. We then make further generalization to either (i) an arbitrary number of additional isosinglets mixing with nonet mesons, or (ii) an arbitrary number of mesons with common J mixing with an additional...

The Schwinger Action Principle and Its Applications to Quantum Mechanics