Searcharxiv⌕ Search

arXiv subjects

J. S. Dowker

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

At least 19 recordsLinked to original sources
arXiv2024

Note on entanglement and edge modes

A recent numerical evaluation of the spherical universal log coefficient in the Maxwell free--energy and its decomposition into bulk and edge contributions via a bounded hyperbolic geometry mode calculation is shown to be equivalent to an existing compact formulation for $p$--forms, at $p=1$, on a conically deformed sphere. The edge mode seems to be a ghost (p-1)-form. Some numbers are given. Conformally covariant, higher derivative propagation is treated and a dynamical origin for the bulk contribution is suggested, The degrees of freedom of the Kalb--Ramond field are briefly discussed.

hep-th↗
arXiv2024

On the vacuum energy in the Einstein Universe and the conformal anomaly

An oldish question is resurrected concerning the significance of the ambiguous `b-type' terms encountered in calculations of the vacuum, Casimir energy on the Einstein Universe for conformally coupled scalar fields. Some remarks in the literature are hopefully clarified and the relevance of much earlier evaluations is pointed out. A consistency principle is suggested.

hep-th↗
arXiv2024

Casimir energy of hyperbolic elements

The contribution, E, of hyperbolic elements to the scalar Casimir energy on a compact quotient of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. Due to the proliferation of prime closed geodesics, the series form for the Casimir energy has an IR divergence. The expression for E is given as a sum of polylogarithms which allows the divergence to be isolated and rendered finite by an {\it ad hoc} Ramanujan renormalisation. The remaining part of E is computed using the specific lower length spectrum of the (2,3,7) triangle and a universal asymptotic form for larger lengths. The tentative value of E found is such as to make the total conformal Casimir energy on the triangle probably negative.

hep-th↗
arXiv2023

Casimir energy for elliptic fixed points

The contribution of elliptic fixed points to the scalar Casimir energy on compact quotients of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. The expression involves derivatives of two-dimensional Barnes zeta-functions which are reduced to Hurwitz zeta-functions for numerical purposes. The values are all positive for any elliptic order.

math.SP↗
arXiv2023

A note on the functional determinant of higher-derivative scalar fields on sphere products

It is shown that the functional determinant ($\sim$ effective action) for a scalar field propagating on the mixed signature product of unit spheres, S$^q\times$S$^p$, according to the GJMS operator, depends, if $d$ is odd, only on $d=p+q$ and on whether $p$ is even or odd. In the first case the effective action equals twice the standard quantity on S$^d$ and vanishes in the second.

hep-th↗
arXiv2023

Calculation of the multiplicative anomaly

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 terms of that for just two of the factors and discuss the specific cases of the sphere and hemisphere. The difference of Neumann and Dirichlet quantities on the hemisphere is equal to that for spin-1/2 on the rim. This is proved generally.

hep-th↗
arXiv2023

Note on a numerical equality regarding the eta invariant on Berger spheres

The Dirac APS eta invariant on a Berger sphere of dimension $2n-1$ is discovered, numerically, to coincide, up to spin factors, with the Dirac conformal anomaly on a round sphere of even dimension, $n$. The analytical expression, given in terms of a generalised Bernoulli polynomial, is shown to equal a known conjecture for the eta invariant. Weingart's generating function is also obtained with no extra work.

math.DG↗
arXiv2023

Algebraic derivation of some theorems concerning contact structures on the 3-sphere

Two theorems involving curl eigenfields on the 3--sphere are obtained using angular momentum theory. Spinor hyperspherical harmonics are shown to form an explicit, convenient basis. In particular, a spin--one vector calculus is reviewed. An easy proof of the vanishing of `odd' eigenfields is given and related to the sign change of fermionic spinors under 2$π$ rotations. The theorem that curl eigenfields with constant norm have to be proportional to a fundamental eigenfield (Hopf field) is also rapidly obtained. Attention is drawn to the relevance of early work of Schrödinger on Maxwell theory in an expanding universe.

math.DG↗
arXiv2023

A discrete Funk-Hecke theorem

A discrete Funk--Hecke formula is set up using the analogy between ordinary and operator spherical harmonics. It is the fuzzy sphere analogue of the conventional theory. An example is related, in the classical limit, to the Rayleigh partial wave expansion.

hep-th↗
arXiv2023

Note on an improved classical limit of Clebsch-Gordan coefficients

A symmetrising shift employed by Frenkel and Hartnoll in the approximate computation of the elements of matrix spherical harmonics is further explored and shown to be related to the permutation symmetry of 3-j symbols yielding an extension of the Edmonds classical limit. Some graphs are displayed.

hep-th↗
arXiv2023

On the limiting behaviour of the su(N) structure constants

The details are expounded of an old treatment of the limit of the su(N) structure constants as N tends to infinity. A recently derived parity property of the series expansion is shown to be the same as the known mirror symmetry of 6-j symbols.

hep-th↗
arXiv2022

On the bulk block expansion for a monodromy defect

For a free--field flat monodromy defect, a formula for the finite part of the correlator is obtained as a double power series in $(1-x)$ and $(1-\ol x)$ where $x$ and $\ol x$ are lightcone coordinates. It takes the particular form of a series in $(1-x)$ with coefficients finite sums of hypergeometric functions of $1-\ol x$ and is identified with a bulk block expansion. A simple expression for the coefficient of the $(1-x)^n(1-\ol x)^m$ term is thereby found as an explicit function of the flux and dimension. Some typical examples are presented.A transformation allows the bulk block expansion to be written as an Appell $F_3$ function which has simplifying consequences.

hep-th↗
arXiv2022

Further on the Aharonov-Bohm Green function: the coincidence limit

For a scalar CFT with a monodromy defect, a `subtracted Green function' is derived in terms of an Appell $F_1$ function. A conjectured relation of Gimenez-Grau and Liendo is thereby proved and extended and shown to hold for generalised free fields. A possible means of determining the bulk block expansion is outlined. Finite coincidence limits are expressed as combinations of Beta functions.

hep-th↗
arXiv2022

On the Green function for an Aharonov-Bohm flux tube

An earlier contour expression for the Green function of a free complex scalar field in the presence of a conical singularity with localised magnetic flux is shown to yield expressions for the field correlator and defect block expansions that have been more recently found in connection with monodromy defects in conformal field theory. The Green function appears as the Picard integral representation of the Appell $F_1$ function. This is shown to transform into a confluent Horn function, corresponding to a different defect block expansion. Other transformations are discussed.

hep-th↗