Related papers: Spherical Dirac GJMS operator determinants

We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$.…

Normality of the Dirac operator is shown to be necessary for chiral properties. From the global chiral Ward identity, which in the continuum limit gives the index theorem, a sum rule results which constrains the spectrum. The…

We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet-to-Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric…

We consider a semi-classical Dirac operator in arbitrary spatial dimensions with a smooth potential whose partial derivatives of any order are bounded by suitable constants. We prove that the distribution kernel of the inverse operator…

For a 4-D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality…

The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…

In this article, we present the symmetry group of a global slice Dirac operator and its iterated ones. Further, the explicit forms of intertwining operators of the iterated global slice Dirac operator are given. At the end, we introduce a…

Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…

It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence two Killing tensors. The role of these operators in the theory…

We construct weighted GJMS operators on smooth metric measure spaces, and prove that they are formally self-adjoint. We also provide factorization formulas for them in the case of quasi-Einstein spaces and under Gover--Leitner conditions.

Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the…

Several determinants with gamma functions as elements are evaluated. This kind of determinants are encountered in the computation of the probability density of the determinant of random matrices. The s-shifted factorial is defined as a…

The functional determinant multiplicative anomaly, or defect, is more closely investigated and explicit forms for products of linear operators are produced. I also present formulae for the defect of products of second order operators in…

Using the overlap formulation, we calculate the fermionic determinant on the lattice for chiral fermions with twisted boundary conditions in two dimensions. When the lattice spacing tends to zero we recover the results of the usual…

We show that the GJMS operators of a special Einstein product factor as a composition of second- and fourth-order differential operators. In particular, our formula applies to the Riemannian product $H^{\ell} \times S^{d-\ell}$. We also…

For an even dimensional, compact, conformal manifold without boundary we construct a conformally invariant differential operator of order the dimension of the manifold. In the conformally flat case, this operator coincides with the critical…

In this work, we use semigroup integral to evaluate zeta-function regularized determinants. This is especially powerful for non--positive operators such as the Dirac operator. In order to understand fully the quantum effective action one…

In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…

The goal of the present paper is to calculate the determinant of the Dirac operator with a mass in the cylindrical geometry. The domain of this operator consists of functions that realize a unitary one-dimensional representation of the…

A new proof of the conformal covariance of the powers of the flat Dirac operator is obtained. The proof uses their relation with the Knapp-Stein intertwining operators for the spinorial principal series. We also treat the compact picture,…