Related papers: Dirac-Sobolev inequalities and estimates for the z…
We investigate $L^1\to L^\infty$ dispersive estimates for the Dirac equation with a potential in four spatial dimensions. We classify the structure of the obstructions at the thresholds as being composed of an at most two dimensional space…
In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a…
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…
Starting with a new theory of symmetries generated by isometries in field theories with spin, one finds the generators of the spinor representation in backgrounds with a given symmetry. In this manner one obtains a collection of conserved…
We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main…
We assume that the manifold with boundary, X, has a Spin_C-structure with spinor bundle S. Along the boundary, this structure agrees with the structure defined by an infinite order integrable almost complex structure and the metric is…
This paper is concerned with the zero mode equation $D_g\varphi=iA\cdot\varphi$ on closed spin manifold $(M^n,g,\sigma)$ of positive scalar curvature. Here $A$ is a real one form on $M$. We proved that if $(\varphi, A)$ is a non trivial…
We introduce the Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$ for Fourier integral operators for $0<p<1$, thereby extending earlier constructions for $1\leq p\leq \infty$. We then establish various properties of these spaces,…
In this paper we work in the `split' discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions, defined on the grid Z^m, of the discrete Dirac operator D, involving both forward and backward…
We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…
The one-dimensional spin-orbital model is studied by means of Abelian bosonization. We derive the low-energy effective theory which enables us to study small deviations from the SU(4) symmetric point. We show that there exists a massless…
By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex…
We obtain a vanishing theorem for the kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base…
Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $\Gamma$ of orientation-preserving isometries acts freely, so that the quotient $X=M/\Gamma$ is compact. We prove a vanishing theorem for a half-kernel of…
In this paper we consider the Dirac spinor field in interaction with a background of electrodynamics and torsion-gravity; by performing the polar reduction we acquire the possibility to introduce a new set of objects that have the…
Motivated by a recent conjecture of Misumi and Yumoto relating the number of zero modes of lattice Dirac operators to the sum of the Betti numbers of the underlying spacetime manifold, we study formal naive Dirac operators on a class of…
We give an optimal upper bound for the first eigenvalue of the untwisted Dirac operator on a compact symmetric space G/H with rk G-rk H\le 1 with respect to arbitrary Riemannian metrics. We also prove a rigidity statement.
There are gauge-transformation operators applicable to massless spin-1/2 particles within the little-group framework of internal space-time symmetries of massive and massless particles. It is shown that two of the $SL(2,c)$ spinors are…
We get decay rate of higher derivatives of nonlinear massless Dirac equations with a kind of "good" spin null form. The method we rely on is similar to that of Li and Zang. However, they only give the decay rate of solution itself to…
We derive a limiting absorption principle on any compact interval in $\mathbb{R} \backslash \{0\}$ for the free massless Dirac operator, $H_0 = \alpha \cdot (-i \nabla)$ in $[L^2(\mathbb{R}^n)]^N$, $n \geq 2$, $N=2^{\lfloor(n+1)/2\rfloor}$,…