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Recent results concerning the relation of topology and low-lying fermion modes are summarized. 1.

We consider non-topological, ”bell-shaped ” localized and regular solutions available in some 1+1 dimensional scalar field theories. Several properties of such solutions are studied, namely their stability and the occurence of fermion bound states in the background of a kink and a kink

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My project computed the one loop fermion self-energy for massless Dirac + Einstein in the presence of a locally de Sitter background. I employed dimensional regularization and obtain a fully renormalized result by absorbing all divergences with Bogliubov, Parasiuk, Hepp and Zimmermann (BPHZ

Recent lattice data indicates that volume occupied by topological fermionic modes shrinks to zero in the continuum limit of vanishing lattice spacing. The data apparently cannot be accommodated within, say, conventional instanton model. We review field-theoretic arguments which demonstrate

We consider instanton-induced high energy processes in an electroweak-type model. Multifermion final states are taken into account in Gauss approximation. Unlike previous results we calculate nonzero fermion modes contribution to cross-section by straightforward procedure. This contribution can

We evaluate the eigenvalues of Dirac operator in the background of instanton-antiinstanton configuration (I-Ī), in a simple (1+0)-dimensional model, and find that quasizero-mode disappears for the closely localized I-Ī configurations. This result suggests that the configurations which are dominant

Abstract not found

We investigate the effects of low-lying fermion modes on the QCD partition function in the ǫ-regime. With the overlap Dirac operator we calculate several tens of low-lying fermion eigenvalues on the quenched lattice. By partially incorporating the fermion determinant through the truncated