## About

13

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Education

September 1987 - August 1992

September 1982 - April 1987

## Publications

Publications (13)

The use of microlocal analysis is considered in proving renormalizability of a particular minimal SME model, as well as of a model of scalar tachyons.

A quantum field model for Dirac-like tachyons respecting a frame-dependent interpretation rule, and thus inherently breaking Lorentz invariance, is defined. It is shown how the usual paradoxa ascribed to tachyons, instability and acausality, are resolved in this model, and it is argued elsewhere that Lorentz symmetry breaking is necessary to permit...

Presented is a framework for viewing nonlocal behaviour in the context of quantum field theory, while maintaining a consistent semblance of causality. The framework is comprised of a model for a Klein-Gordon quantum field theory of tachyons on Minkowski spacetime, without exponentially growing modes, and yet with a sensible notion of causality. (Th...

We use microlocal arguments to suggest that Lorentz symmetry breaking must occur in a reasonably behaved tachyonic quantum field theory that permits renormalizability. In view of this, we present a scalar tachyonic quantum field model with manifestly broken Lorentz symmetry and without exponentially growing/decaying modes. A notion of causality, in...

We calculate the phase space factor for a two-body decay in which one of the products is a tachyon. Two threshold conditions, a lower and an upper one, are derived in terms of the masses of the particles and the speed of a preferred frame. Implicit in the derivation is a consistently formulated quantum field theory of tachyons in which spontaneous...

For the two-point distribution of a quasi-free Klein-Gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space-time we prove the equivalence of (1) the global Hadamard condition, (2) the property that the Feynman propagator is a distinguished parametrix in the sense of Duistermaat and Hörmander, and (3) a...

We prove that if a reference two-point distribution of positive type on a time orientable curved space-time (CST) satisfies a certain condition on its wave front set (the “classP
M,g
condition”) and if any other two-point distribution (i) is of positive type, (ii) has the same antisymmetric part as the reference modulo smooth function and (iii) has...

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, \(\), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as ‘past terminal accumulation points’ of the horiz...

For the two-point distribution of a quasi-free Klein-Gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space-time we prove the equivalence of (1) the global Hadamard condition, (2) the property that the Feynman propagator is a distinguished parametrix in the sense of Duistermaat and Hörmander, and (3) a...

We prove that if a reference two-point distribution of positive type on a time orientable curved space-time (CST) satisfies a certain condition on its wave front set (the "class PM,g condition") and if any other two-point distribution (i) is of positive type, (ii) has the same antisymmetric part as the reference modulo smooth function and (iii) has...

We interpret the global Hadamard condition for a two-point distribution
of a Klein-Gordon neutral scalar quantum field model on an arbitrary
globally hyperbolic curved space-time in terms of distinguished
parametrices (of Duistermaat and Hormander) and a wave front set
spectrum condition. Microlocal results by Duistermaat and Hormander such
as the...

We correct the calculation for the ''inertial viewpoint'' in Unruh and Wald (Phys. Rev. D 25, 942 (1982)), without altering the conclusions of that paper.

## Projects

Projects (2)

I am studying the Bergman kernel for the annulus r<|z|<1 (0<r<1) in C, the complex plane. I was made aware of the Bergman kernel and metric on domains (open, connected subsets) of C through Steven G. Krantz's book, "Geometric Function Theory" (Birkhaeuser: Boston, 2006), especially Section 1.4, where the annulus case is touched on. For the case of the unit disk, the Bergman metric reduces to the Poincare metric, but for the annulus, the expression for the Bergman kernel involves a Weierstrass elliptic function. Also, Bergman (in his book "The Kernel Function and Conformal Mapping", Am. Math. Soc.: Providence, RI, 1970) defines this metric g from the kernel in a way that appears different than the way Krantz chooses (apparently to ensure that g is Kaehler). Krantz's statement that the calculation is "intractable" is mystifying to me, since Bergman already wrote down the answer in 1970 (or possibly earlier), which I could verify using a formula for the Fourier series representation of this elliptic function found in a reference on elliptic functions. I am still seeking to clarify this apparent ambiguity in the choice of metric, as well as to understand how to describe the geodesics for this metric space.