Related papers: Local Boundary Conditions for the Dirac Operator a…
The contribution of physical degrees of freedom to the one-loop amplitudes of Euclidean supergravity is here evaluated in the case of flat Euclidean backgrounds bounded by a three-sphere, recently considered in perturbative quantum…
We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime, focusing on a (1+1)-dimensional case in which the evolution of the scale factor is set by the equations of…
We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a…
We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary…
We develop novel first-kind boundary integral equations for Euclidean Dirac operators in 3D Lipschitz domains comprising square-integrable potentials and involving only weakly singular kernels. Generalized Garding inequalities are derived…
We consider the Wheeler-DeWitt equation $H\psi=0$ in a suitable Hilbert space. It turns out that this equation has countably many solutions $\psi_i$ which can be considered as eigenfunctions of a Hamilton operator implicitly defined by $H$.…
DeWitt's suggestion that the wave function of the universe should vanish at the classical big-bang singularity is here considered within the framework of one-loop quantum cosmology. For pure gravity at one loop about a flat four-dimensional…
We study the family of operators $\{\mathcal{R}_a\}_{a\in [0,+\infty)}$ associated to the Robin-type problems in a bounded domain $\Omega\subset\mathbb{R}^2$ $$ \begin{cases} -\Delta u = f & \text{in } \Omega, \\ 2 \bar \nu \partial_{\bar…
In this paper, we investigate how the gravitational field generated by a four-dimensional electrovacuum cosmological space-time influences the dynamics of fermionic fields governed by the Dirac equation, while also considering the effects…
This paper is devoted to mathematical and physical properties of the Dirac operator and spectral geometry. Spin-structures in Lorentzian and Riemannian manifolds, and the global theory of the Dirac operator, are first analyzed. Elliptic…
About a decade ago the present author in collaboration with Daniel Grumiller presented an `unexpected theoretical discovery' of spin one-half fermions with mass dimension one [JCAP 2005, PRD 2005]. In the decade that followed a significant…
Canonical quantization of spherically symmetric initial data which is appropriate to classical interior black hole solutions in four dimensions is carried out and solved exactly without gauge fixing the remaining kinematic Gauss Law…
In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in Euclidean space by combining a positive mass theorem and the construction of quasi-spherical metrics. As a direct consequence of this…
We consider $\text{SU}(2)$ quantum chromodynamics in $1+1$ dimensions with a single quark in the spin $J$ representation of the gauge group and study the theory in the large $J$ limit where the gauge coupling $g^2 \to 0$ and $J \to \infty$…
The anomalies of a very general class of non local Dirac operators are computed using the $\zeta$-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms…
This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a…
We re-visit the eigenvalue estimate of the Dirac operator on spin manifolds with boundary in terms of the first eigenvalues of conformal Laplace operator as well as the conformal mean curvature operator. These problems were studied earlier…
This work pioneers the quantization of primordial fermion perturbations in hybrid Loop Quantum Cosmology (LQC). We consider a Dirac field coupled to a spatially flat, homogeneous, and isotropic cosmology, sourced by a scalar inflaton, and…
We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either in the domain with a MIT-bag type boundary condition or in…
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by…