Papers by Marek J Radzikowski
We calculate the phase space factor for a two-body decay in which one of the products is a tachyo... more 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 Lorentz symmetry breaking occurs. The result is to be contrasted with a parallel calculation by Hughes and Stephenson, which, however, implicitly adheres to strict Lorentz invariance of the underlying quantum field theory and produces the conclusion that there is no threshold for this process.
We interpret the global Hadamard condition for a two-point distribution of a Klein-Gordon neutral... more 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 propagation of singularities theorem and the uniqueness of distinguished parametrices are employed in the proof. Using a smoothing, positivity-preserving pseudo -differential operator, one obtains a local-to-global singularity theorem, generalizing a conjecture by Kay that for quasi -free Klein-Gordon states, local Hadamard implies global Hadamard. This theorem relies on a general wave front set spectrum condition for the two-point distribution; a counterexample is given on Minkowski space when this condition is violated. We postulate a wave front set condition for any m-point distribution on a space-time and show consistency up to C^infty with the usual spectrum condition on Minkowski space and exact correspondence with this condition in the scaling limit. Axioms implying a spin-statistics theorem are suggested for quantum field models on curved space-time.
CPT and Lorentz Symmetry, 2014
CPT and Lorentz Symmetry - Proceedings of the Fifth Meeting, 2010
A quantum field model for Dirac-like tachyons respecting a frame-dependent interpretation rule, a... more 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 perturbative renormalizability and causality. Elimination of negative-normed states results in only left-handed particles and right-handed antiparticles, suitable for describing the neutrino. In this context the neutron beta decay spectrum is calculated near the end point for large, but not ultrarelativistic preferred frame speed, assuming a vector weak interaction vertex.
Physical review D: Particles and fields, Jan 15, 1988
We correct the calculation for the ''inertial viewpoint&a... more 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.
We use microlocal arguments to suggest that Lorentz symmetry breaking must occur in a reasonably ... more 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 which anti-telephones are excluded, and which is viewed as a
Presented is a framework for viewing nonlocal behaviour in the context of quantum field theory, w... more 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. (The latter may be expressed as a ``no
We calculate the phase space factor for a two-body decay in which one of the products is a tachyo... more 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
Communications in Mathematical Physics, 1997
We prove two theorems which concern difficulties in the formulation of the quantum theory of a li... more We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M, g ab ), 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
Communications in Mathematical Physics, 1996
We prove that if a reference two-point distribution of positive type on a time orientable curved ... more 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 0hi i9 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 the same local singularity structure, then it has the same global singularity structure. In the proof we use a smoothing, positivity-preserving pseudodifferential operator the support of whose symbol is restricted to a certain conic region which depends on the wave front set of the reference state. This local-toglobal theorem, together with results published elsewhere, leads to a verification of a conjecture by Kay that for quasi-free states of the Klein-Gordon quantum field on a globally hyperbolic CST, the local Hadamard condition implies the global Hadamard condition. A counterexample to the local-to-global theorem on a strip in Minkowski space is given when the class &ht, g condition is not assumed.
For the two-point distribution of a quasi-free Klein-Gordon neutral scalar quantum field on an ar... more 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 new property referred to as the wave front set spectral condition (WFSSC), because it is reminiscent of the spectral condition in axiomatic quantum field theory on Minkowski space. Results in micro-local analysis such as the propagation of singularities theorem and the uniqueness up to C ∞ of distinguished parametrices are employed in the proof. We include a review of Kay and Wald's rigorous definition of the global Hadamard condition and the theory of distinguished parametrices, specializing to the case of the Klein-Gordon operator on a globally hyperbolic space-time. As an alternative to a recent computation of the wave front set of a globally Hadamard two-point distribution on a globally hyperbolic curved space-time, given elsewhere by Köhler (to correct an incomplete computation in [34]), we present a version of this computation that does not use a deformation argument such as that used in Fulling, Narcowich and Wald and is independent of the Cauchy evolution argument of Fulling, Sweeny and Wald (both of which are relied upon in Köhler's proof). This leads to a simple micro-local proof of the preservation of Hadamard form under Cauchy evolution (first shown by Fulling, Sweeny and Wald) relying only on the propagation of singularities theorem. In another paper [33], the equivalence theorem is used to prove a conjecture by Kay that a locally Hadamard quasi-free Klein-Gordon state on any globally hyperbolic curved space-time must be globally Hadamard.
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Papers by Marek J Radzikowski