Lüders and Pauli proved the $\mathcal{CPT}$ theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why $\mathcal{CPT}$ is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the $\mathcal{CPT}$ transform of any relativistic field (...) without calculating $\mathcal{C}$ , $\mathcal{P}$ and $\mathcal{T}$ separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the $\mathcal{CPT}$ theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary. (shrink)

This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The infrared divergence is associated with the inequivalence of the Hilbert spaces associated with the free Hamiltonian and with the complete Hamiltonian. Infrared divergences that are visible in the perturbative description disappear in the space of the clothed electrons. In this model when (...) the Hamiltonian is expressed in terms of the “physical” fields that create the electron together with its cloud of soft photons, the variational principle suggested earlier can be applied. At finite time the Heisenberg field of the model acts in the space of the perturbative electron together with a finite number of perturbative photons, while the “physical” field can be chosen to act in the space of the exact (“physical”) electron eigenstates together with a finite number of physical photons. The space of the physical (or clothed) electron states can be chosen to be a Fock space. (shrink)

Quons are particles characterized by the parameter q, which permits smooth interpolation between Bose and Fermi statistics; q = 1 gives bosons, q = -1 gives fermions. In this paper we give a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form ffb, where f is fermion-like and b is boson-like. We show that q f 2 = qb. In particular, we relate the bound on qγ for photons to the bound on (...) qe for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of this argument suggests that all particles are fermions or bosons to a high precision. (shrink)

A Christian approach to the issues that constitute bioethics is inevitable for us who cherish the truth of historic, creedal, trinitarian Christianity. Scripture teaches and the Greek and Latin Church Fathers as well as the Reformers aver that man, created in the image of God, has an inherent, if vestigial, sense of right and wrong and a conscience however marred by the fall and by rebellion. We must believe that we share this most basic ecumenism with all humanity, not because (...) of rational observation and analysis of nature, but because Scripture reveals it. We who are convinced of the truth of historic, creedal, trinitarian Christianity have a high view of Scripture and hold it to be infallible and utterly trustworthy irrespective of the importance we assign to our specific post-biblical traditional distinctives. This is a narrower but much more vital ecumenism than the first. Faithful adherence to Scripture inevitably manifests itself in remarkably similar priorities and values, often, lamentably, not because of, but in spite of, ourselves. (shrink)

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

The present study tested the hypothesis that centrality of religiosity as defined as the position of an individual’s religious construct system in personality moderates the relationship between the experience of forgiveness by God and forgivingness for others. Participants completed measures of forgiveness by God, forgivingness, and centrality of religiosity. The moderating hypothesis was tested by treating centrality of religiosity both as a continuous variable and as a categorical variable with reference to a typological distinction. Results indicate that centrality of religiosity (...) moderates the positive relationship between forgiveness by God and forgivingness for others, implying that this relation only occurs if the religious construct system is in a central position in personality, but not if it is in a subordinate position. These results underline the importance of considering centrality of religiosity as an individual difference variable. (shrink)