• Home
  • Marek J. Radzikowski
Marek J. Radzikowski

Marek J. Radzikowski

Ph.D.

About

13
Publications
5,726
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
870
Citations
Additional affiliations
January 2017 - April 2017
Trinity Western University
Position
  • Instructor
Description
  • Taught Modern Physics, Particle Physics and intermediate Classical Mechanics.
September 2011 - December 2016
The American University of Afghanistan
Position
  • Professor
Description
  • Taught first year physics, mathematics and statistics courses
January 2009 - April 2010
University of British Columbia - Vancouver
Position
  • Instructor
Description
  • Instructor for first year Physics labs
Education
September 1987 - August 1992
Princeton University
Field of study
  • Applied and Computational Mathematics
September 1982 - April 1987
University of British Columbia - Vancouver
Field of study
  • Engineering Physics

Publications

Publications (13)
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
Full-text available
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...
Article
Full-text available
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.

Network

Cited By

Projects

Projects (2)
Project
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.