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J. S. Dowker

Publications and source records attributed to J. S. Dowker.

At least 109 records · Page 6Linked to original sources
arXiv1999

Magnetic fields and factored two-spheres

A magnetic monopole is placed at the centre of a 3-ball whose surface, S, is tiled by the symmetry group, G, of a regular solid. The quantum mechanics on the two-dimensional quotient, S/G, is developed and the monopole charge is found to be quantized in the expected manner. The heat-kernels and zeta-functions are evaluated and the Casimir energies computed as examples of the formalism. Numerical approaches to the calculation of the derivative of the Barnes zeta-function are presented.

hep-th↗
arXiv1999

Effective actions on the squashed three-sphere

The effective actions of a scalar and massless spin-half field are determined as functions of the deformation of a symmetrically squashed three-sphere. The extreme oblate case is particularly examined as pertinant to a high temperature statistical mechanical interpretation that may be relevant for the holographic principle. Interpreting the squashing parameter as a temperature, we find that the effective `free energies' on the three-sphere are mixtures of thermal two-sphere scalars and spinors which, in the case of the spinor on the three-sphere, have the `wrong' thermal periodicities. However the free energies do have the same leading high temperature forms as the standard free energies on the two-sphere. The next few terms in the high-temperature expansion are also explicitly calculated and briefly compared with the Taub-Bolt-AdS bulk result.

hep-th↗
arXiv1998

The $a_{3/2}$ heat kernel coefficient for oblique boundary conditions

We present a method for the calculation of the $a_{3/2}$ heat kernel coefficient of the heat operator trace for a partial differential operator of Laplace type on a compact Riemannian manifold with oblique boundary conditions. Using special case evaluations, restrictions are put on the general form of the coefficients, which, supplemented by conformal transformation techniques, allows the entire smeared coefficient to be determined.

hep-th↗
arXiv1998

Smeared heat-kernel coefficients on the ball and generalized cone

We consider smeared zeta functions and heat-kernel coefficients on the bounded, generalized cone in arbitrary dimensions. The specific case of a ball is analysed in detail and used to restrict the form of the heat-kernel coefficients $A_n$ on smooth manifolds with boundary. Supplemented by conformal transformation techniques, it is used to provide an effective scheme for the calculation of the $A_n$. As an application, the complete $A_{5/2}$ coefficient is given.

hep-th↗
arXiv1998

Conformal anomaly in 2d dilaton-scalar theory

The discrepancy between the anomaly found by Bousso and Hawking (hep-th/9705236) and that of other workers is explained by the omission of a zero mode contribution to the effective action.

hep-th↗
arXiv1997

The C_2 heat-kernel coefficient in the presence of boundary discontinuities

We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel coefficient is derived in the case of a scalar field with Dirichlet and Robin boundary conditions. The coefficient is then determined using conformal symmetry and evaluation on some specific manifolds. For the Robin case a perturbation technique is also developed and employed. The contributions to the smeared heat-kernel coefficient and cocycle function are calculated. Some incomplete results for spinor fields with mixed conditions are also presented.

hep-th↗
arXiv1997

Heat-kernel coefficients for oblique boundary conditions

We calculate the heat-kernel coefficients, up to $a_2$, for a U(1) bundle on the 4-Ball for boundary conditions which are such that the normal derivative of the field at the boundary is related to a first-order operator in boundary derivatives acting on the field. The results are used to place restrictions on the general forms of the coefficients. In the specific case considered, there can be a breakdown of ellipticity.

hep-th↗
arXiv1996

Spinors and forms on generalised cones

A method is presented, and used, for determining any heat-kernel coefficient for the form-valued Laplacian on the $D$-ball as an explicit function of dimension and form order. The calculation is offerred as a particular application of a general technique developed earlier for obtaining heat-kernel coefficients on a bounded generalised cone which involves writing the sphere and ball \zfs, and coefficients, in terms of Barnes \zfs\ and generalised Bernoulli polynomials. Functional determinants are computed. Spinors are also treated by the general method.

hep-th↗
arXiv1996

Heat-kernels and functional determinants on the generalized cone

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions thereby placed on the $A_{5/2}$ coefficient. The computation of functional determinants is also addressed. General formulas are given and known results are incidentally, and rapidly, reproduced.

hep-th↗
arXiv1995

Functional determinants on Moebius corners

A general method of finding functional determinants is presented that depends on the asymptotic behaviour of the resolvent. Its application to the case of a bounded trihedral corner for which the eigenvalues are known only implicitly is outlined and a generalisation of Barnes' product form of multiple gamma functions is given

hep-th↗
arXiv1995

Spin on the 4-ball

Using known mode properties, the functional determinant for massless spin-half fields on the Euclidean 4-ball is calculated and shown to be different for spectral (nonlocal) and mixed (local) boundary conditions. The local result agrees with that from a conformal argument. Some higher-spin results are also given.

hep-th↗
arXiv1995

Robin conditions on the Euclidean ball

Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions. The method involves a large mass asymptotic limit which is carried out in detail for d=2 and d=4 incidentally producing some specific summations and identities. Extensive use is made of the Watson-Kober summation formula.

hep-th↗
arXiv1995

Oddball determinants

A simplified direct method is described for obtaining massless scalar functional determinants on the Euclidean ball. The case of odd dimensions is explicitly discussed.

hep-th↗
arXiv1995

Further functional determinants

Functional determinants for the scalar Laplacian on spherical caps and slices, flat balls, shells and generalised cylinders are evaluated in two, three and four dimensions using conformal techniques. Both Dirichlet and Robin boundary conditions are allowed for. Some effects of non-smooth boundaries are discussed; in particular the 3-hemiball and the 3-hemishell are considered. The edge and vertex contributions to the $C_{3/2}$ coefficient are examined.

hep-th↗
arXiv1994

Functional determinants and effective actions:Corrigenda

Some calculational errors in expressions derived previously by the first author for the effective action, or equivalently for the functional determinant, on sectors of a spherical cap are corrected. The formula for the change in the effective action under Weyl rescalings in the three dimensional case is also amended.

hep-th↗