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Δελτίον Χριστιανικής Αρχαιολογικής Εταιρείας, 1999
In these notes I would like to try and give an introduction to the quantum mechanical theory of the photon. The treatment I give is in the spirit of a treatment you can find in Dirac's quantum mechanics monograph, The Principles of Quantum Mechanics. I believe that Dirac was one of the first (if not the first) person to work out these ideas. Along the way, we will be generalizing the way we use quantum mechanics in a non-trivial way. More precisely, the way we model nature using the rules of quantum mechanics will change significantly, although the rules themselves will not actually change. Let us begin by setting the stage for this generalization. Consider the well-known processes of emission and absorption of photons by atoms. The processes of emission and absorption of photons by atoms cannot, ultimately, be accommodated in the usual quantum mechanical models based on particle mechanics. Instead, one must use a new class of models that go under the heading of quantum field theory. The reasons for this necessity are relatively simple if one focuses on spontaneous emission in atoms. This is where an atom in an excited state will spontaneously decay to a lower energy state (and emit one or more photons). First, we all know that the electron states we use to characterize atoms are the stationary states, which are energy eigenstates. But stationary states have the property that all their observable features are time independent. If an atomic electron occupying an atomic energy level were truly in a stationary state there could never be any spontaneous emission since a stationary state has no time dependent behavior. The only way out of this conundrum is to suppose that atomic energy levels are not really stationary states once you take into account the interaction of photons and electrons. But now consider emission of a photon by an atomic electron. The initial state of the system has an electron. The final state of the system has an electron and a photon. Now, in the usual quantum mechanical formalism for particles the number of particles is always fixed. Indeed, the normalization of the wave function for a particle (or for particles) can be viewed as saying that the particle (or particles) is (or are) always somewhere. Evidently, such a state of affairs will not allow us to treat a particle such as a photon that can appear and disappear. Moreover, it is possible to have atomic transitions in which more than one photon appears/disappears. Clearly we will not be able to describe such processes using the quantum mechanical models developed thus far. If this isn't surprising enough, I remind you that there exist situations in which a photon may " transform " into an electron-positron pair and, conversely, in which an electron-positron can turn into a photon. So even electrons are not immune from the appearance/disappearance phenomenon.
Δελτίον Χριστιανικής Αρχαιολογικής Εταιρείας, 2011
Introduction, 2011
ΑνΑρχές οι µεταφράσεις µας ακόµα και οι καλύτερες ξεκινούν από µια εσφαλµένη αρχή θέλουν να γερµανοποιήσουν τα ινδικά τα ελληνικά τα αγγλικά αντί να ινδοποιούν, ελληνοποιούν, αγγλοποιούν τα γερµανικά […] το θεµελιώδες λάθος του µεταφραστή είναι ότι γαντζώνεται στην κατάσταση στην οποία τυχαίνει να βρίσκεται η γλώσσα του αντί να της επιτρέπει να τεθεί δυναµικά σε κίνηση από την ξένη γλώσσα. […] πρέπει να εµβαθύνει τη δική του γλώσσα µέσω της ξένης […] Rudolf Pannwitz όπως παρατίθεται στον Μπένγιαµιν
Byzantina Symmeikta, 2020
ThE gEogRaphy of ThE pRovincial adminisTRaTion of ThE ByzanTinE EmpiRE (ca 600-1200): i.1. ThE apoThEkai of asia minoR (7Th-8Th c.) ΑΘΗΝΑ • 2009 • ATHENS Τομοσ 30 volumE ΑφροδιΤη ΠΑσΑλη συμβολη σΤη μελεΤη Τησ σΤηριξεωσ συνεΠΤυγμενων Τρουλλων σΤη μεΤΑβυζΑνΤινη νΑοδομιΑ ΑΘΗΝΑ • 2020 • ATHENS INSTITUTE OF HISTORICAL RESEARCH
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