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تسجيل مستخدم جديدPath Integral and Spectral Representations for Supersymmetric Dirac-Hamiltonians
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The resolvent of supersymmetric Dirac Hamiltonian is studied in detail. Due to supersymmetry the squared Dirac Hamiltonian becomes block-diagonal whose elements are in essence non-relativistic Schrodinger-type Hamiltonians. This enables us to find a Feynman-type path-integral representation of the resulting Greens functions. In addition, we are also able to express the spectral properties of the supersymmetric Dirac Hamiltonian in terms of those of the non-relativistic Schrodinger Hamiltonians. The methods are explicitly applied to the free Dirac Hamiltonian, the so-called Dirac oscillator and a generalization of it. The general approach is applicable to systems with good and broken supersymmetry.
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