A Historical Investigation

Visser, H. [Promotor]Blaug, M. [Promotor

The role of Vitamin D and Parathyroid Hormone in Cardiovascular Health

Visser, M. [Promotor]Brouwer, I.A. [Copromotor

Quantum Interest in (3+1) dimensional Minkowski space

The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture", use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a time-like observer, potentially preventing the existence of exotic phenomena such as "Alcubierre warp-drives" or "traversable wormholes". Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or non-existence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple proof of one version of the Quantum Interest Conjecture in (3+1) dimensional Minkowski space.Comment: V1: 8 pages, revtex4; V2: 10 pages, some technical changes in details of the argument, no change in physics conclusions, this version essentially identical to published versio

Lambda theories of effective lambda models

A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the more general question of whether the equational (resp. order) theory of a non syntactical model M, say Eq(M) (resp. Ord(M)) can be recursively enumerable (= r.e. below). We conjecture that no such model exists and prove the conjecture for several large classes of models. In particular we introduce a notion of effective lambda-model and show that for all effective models M, Eq(M) is different from Lb, and Ord(M) is not r.e. If moreover M belongs to the stable or strongly stable semantics, then Eq(M) is not r.e. Concerning Scott's continuous semantics we explore the class of (all) graph models, show that it satisfies Lowenheim Skolem theorem, that there exists a minimum order/equational graph theory, and that both are the order/equ theories of an effective graph model. We deduce that no graph model can have an r.e. order theory, and also show that for some large subclasses, the same is true for Eq(M).Comment: 15 pages, accepted CSL'0

An algorithm for the Baker-Campbell-Hausdorff formula

A simple algorithm, which exploits the associativity of the BCH formula, and that can be generalized by iteration, extends the remarkable simplification of the Baker-Campbell-Hausdorff (BCH) formula, recently derived by Van-Brunt and Visser. We show that if $[X,Y]=uX+vY+cI$, $[Y,Z]=wY+zZ+dI$, and, consistently with the Jacobi identity, $[X,Z]=mX+nY+pZ+eI$, then $$\exp(X)\exp(Y)\exp(Z)=\exp({aX+bY+cZ+dI})$$ where $a$, $b$, $c$ and $d$ are solutions of four equations. In particular, the Van-Brunt and Visser formula $$\exp(X)\exp(Z)=\exp({aX+bZ+c[X,Z]+dI})$$ extends to cases when $[X,Z]$ contains also elements different from $X$ and $Z$. Such a closed form of the BCH formula may have interesting applications both in mathematics and physics. As an application, we provide the closed form of the BCH formula in the case of the exponentiation of the Virasoro algebra, with ${\rm SL}_2({\rm C})$ following as a subcase. We also determine three-dimensional subalgebras of the Virasoro algebra satisfying the Van-Brunt and Visser condition. It turns out that the exponential form of ${\rm SL}_2({\rm C})$ has a nice representation in terms of its eigenvalues and of the fixed points of the corresponding M\"obius transformation. This may have applications in Uniformization theory and Conformal Field Theories.Comment: 1+8 pages. Comments and refences added. Typos corrected. Version to appear in JHE

Stable gravastars with generalised exteriors

New spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti--de Sitter or de Sitter interior and a Schwarzschild--(anti)--de Sitter or Reissner--Nordstr\"{o}m exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviours of the equation of state for these parameters.Comment: 14 pages, 11 figures, to appear in Classical and Quantum Gravit

Horizon constraints and black hole entropy

To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories as well, the imposition of a "stretched horizon" constraint alters the algebra of symmetries at the horizon, introducing a central term. Standard conformal field theory techniques can then then be used to obtain the asymptotic density of states, reproducing the Bekenstein-Hawking entropy. The microscopic states responsible for black hole entropy can thus be viewed as "would-be pure gauge" states that become physical because the symmetry is altered by the requirement that a horizon exist.Comment: 20 pages, to appear in "The Kerr spacetime: rotating black holes in general relativity," edited by S. Scott, M. Visser, and D. Wiltshire (Cambridge University Press