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Dimensional transmutation in quantum theory
Ebr, Jan ; Hořejší, Jiří (advisor) ; Novotný, Jiří (referee)
This work deals with two models - from the quantum eld theory it is the massless scalar electrodynamics (the so-called Coleman-Weinberg model) and from quantum mechanics it is the contact (-function) potential (in two dimensions) - that are apparently invariant under some sort of scale transformations and thus they, in suitably chosen units, contain only dimensionless parameters. It turns out that even in the quantum-mechanical case one has to add an additional procedure to the formal denition of the model and that the use of dierent physical regulators leads to the same results, that furthermore agree with the predictions of the mathematically rigorous method of self-adjoint operator extensions. In this work, we present detailed calculations supporting this result. Contrary to the common literature, we do so in a straightforward manner, which can be followed step by step (with all the necessary elements of functional analysis summarised in the Appendix). In quantum eld theory we apply a similar approach, when we "rediscover" the results of the abstract functional methods in the ordinary perturbation theory. In its framework, we further show how to obtain predictions also for other quantities than particle masses.
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Phenomenological models inspired by QCD and their use in the analysis of ultra-high energy cosmic rays
Ebr, Jan ; Řídký, Jan (advisor) ; Leitner, Rupert (referee) ; Unger, Michael (referee)
Cosmic rays of energies above 1014 eV are detected mostly indirectly, by observing the extensive air showers they create in the atmosphere. Multiple experiments suggest that the current models of high-energy interactions do not describe the cosmic ray data perfectly, in particular when it comes to the prediction for the number of muons at ground. We present two models aiming to improve the description of the muon component, one based on the addition of particles with small momenta in the local center-of-mass frame of the high-energy hadronic interactions in the shower, the other on the addition of the so-called dark photons to the electromagnetic part of the shower. While we find the latter having no observable consequences, the former improves the agreement between observed and predicted amounts of muons both for the DELPHI cosmic ray data and for the measurements by the Pierre Auger Observatory. We also describe the FRAM telescope, a device used to monitor the atmosphere at the Pierre Auger Observatory, and its applications to the search for anomalous shower profiles and to the measurement of the aerosol content of the atmosphere, which is crucial for the analysis of data obtained by fluorescence detectors. 1
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Dimensional transmutation in quantum theory
Ebr, Jan ; Hořejší, Jiří (advisor) ; Novotný, Jiří (referee)
This work deals with two models - from the quantum eld theory it is the massless scalar electrodynamics (the so-called Coleman-Weinberg model) and from quantum mechanics it is the contact (-function) potential (in two dimensions) - that are apparently invariant under some sort of scale transformations and thus they, in suitably chosen units, contain only dimensionless parameters. It turns out that even in the quantum-mechanical case one has to add an additional procedure to the formal denition of the model and that the use of dierent physical regulators leads to the same results, that furthermore agree with the predictions of the mathematically rigorous method of self-adjoint operator extensions. In this work, we present detailed calculations supporting this result. Contrary to the common literature, we do so in a straightforward manner, which can be followed step by step (with all the necessary elements of functional analysis summarised in the Appendix). In quantum eld theory we apply a similar approach, when we "rediscover" the results of the abstract functional methods in the ordinary perturbation theory. In its framework, we further show how to obtain predictions also for other quantities than particle masses.
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