arXiv subjects

Ali Mostafazadeh

Publications and source records attributed to Ali Mostafazadeh.

183 records · Page 11Linked to original sources

arXiv1993

Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions, and a Supersymmetric Proof of the Index Theorem

The Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The Green's function methods provide a direct derivation of the index formula. Note: This is essentially a new SUSY proof of the index theorem.

hep-th↗

arXiv1993

Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr{\" o}dinger Equation

The quantization of the superclassical system used in the proof of the index theorem results in a factor of $\hbar^{2}R/8 $ in the Hamiltonian. The path integral expression of the kernel is analyzed up to and including 2-loop order. The existence of the scalar curvature term is confirmed by comparing the linear term in the heat kernel expansion with the 2-loop order terms in the loop expansion.

hep-th↗

arXiv1993

Topological Aspects of the Non-adiabatic Berry Phase

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter space is not well-defined at the critical frequency.

hep-th↗