M. Hortaçsu

Zero-energy eigenstates for the Dirac boundary problem

Abstract As an alternative to the method of spherical compactification for the Dirac operator in instanton background fields we study the correct method of “box-quantization”: the Atiyah-Patodi-Singer spectral boundary condition. This is the only self-adjoint boundary condition which respects the charge conjugation property and the γ5 symmetry, apart from the usual breaking due to zero modes. We point out the relevance of this approach to the computation of instanton determinants and other problems involving Dirac spinors.

Properties of solutions in (2+1)-dimensions

We solve the Einstein equations for the 2 + 1 dimensions with and without scalar fields. We calculate the entropy, Hawking temperature and the emission probabilities for these cases. We also compute the Newman-Penrose coefficients for different solutions and compare them.

Dirac Equation in the Background of the Nutku Helicoid Metric

We study the solutions of the Dirac equation in the background of the Nutku helicoid metric. This metric has curvature singularities, which necessitates imposing a boundary to exclude this point. We use the Atiyah-Patodi-Singer [Math. Proc. Cambridge Philos. Soc. 77, 43 (1975)] nonlocal spectral boundary conditions for both the four and the five dimensional manifolds.

Gravitational instantons from minimal surfaces

Physical properties of gravitational instantons which are derivable from minimal surfaces in three-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi type , or E(2), which admits a hidden symmetry due to the existence of a quadratic Killing tensor. It leads to a complete separation of variables in the Hamilton-Jacobi equation for geodesics, as well as in Laplaces equation for a massless scalar field. The scalar Green function can be obtained in closed form, which enables us to calculate the vacuum fluctuations of a massless scalar field in the background of this instanton.

The Quantization of the Gursey Model

Abstract The Gursey model, a conformally invariant pure spinor model in four dimensions, is quantized to result in an asymptotically free theory.

A Pure Spinor Model With Composite Gluons

Abstract A pure spinor model with a non-polynomial interaction with global SU ( n ) symmetry is quantized in the path integral formalism. The model is found to be asymptotically free.

Spurious Effects in Perturbative Calculations

We show spurious effects in perturbativecalculations due to different orderings of inhomogeneousterms while computing corrections to Green functions fortwo different metrics. These effects are not carried over to physically measurable quantities likethe renormalized value of the vacuum expectation valueof the stress-energy tensor.

Vacuum fluctuations of a massless spin- field around multiple cosmic strings

We study the interaction of a massless quantized spinor field with the gravitational field of N parallel static cosmic strings by using a perturbative approach. We show that the presence of more than one cosmic string gives rise to an additional contribution to the energy density of vacuum fluctuations, thereby leading to a vacuum force of attraction between two parallel cosmic strings.

Gauge bosons as composites of fermions

Abstract Non-abelian gauge theories are obtained as effective theories of certain models which at the lagrangian level contain only spinor fields.

Fluctuations of a spherical gravitational impulsive wave

It is shown that quantum fluctuations, in particular vacuum polarization, vanish in the background of a spherical impulsive wave solution of the Einstein field equations, recently found by Nutku and Penrose. The calculation is done in first‐order perturbation theory but arguments are given why it should persist to all orders.