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Optimization of Integration of Promax Training Equipment into Education
Vaško, Petr ; Číka, Petr (referee) ; Škorpil, Vladislav (advisor)
This thesis is focused on familiarization with the instructional device PROMAX, which is an illustrative example of functioning of a private central telephone switchboard, including simulation of the interconnection with the central telephone switchboard. First, the completion including wiring was carried out, the followed by the initial enlivening of the laboratory equipment, and detailed familiarization with its basic functions. After obtaining the requisite knowledge of the device, a comprehensible manual with individual parts of the tutorial system described in detail was elaborated. The emphasis is placed on understanding the problems of functions of individual blocks of the telephone switchboard, the successive modules, and the principle of interconnection. In the following part of the thesis a design of the laboratory tasks for students is carried out. They are designed to practical verification of the performance of the individual blocks, their interconnection and configuration. The attachments which are a part of the thesis contain the model design of the individual laboratory tasks.
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Supersymmetric Quantum Mechanics meets Topology
Kriš, Jakub ; Vaško, Petr (advisor) ; Procházka, Tomáš (referee)
In the first part of this thesis, we will try to get familiar with some of the concepts of supersymmetry (SUSY), starting from the zero-dimensional Quantum Field Theory and apply these concepts to a toy model of (0+1) dimensional QFT otherwise known as Quantum Mechanics. Methods explored in this thesis allow for the computation of path integrals, mainly the partition function and its modification, the Witten Index, which "counts" the difference between bosonic and fermionic states of the SUSY model used. The second part will focus on how this is related to the topology, more precisely the topological invariants, of the manifold (target space). The model in question will be a particular supersymmetric sigma model (σ-model), where the Witten Index is related to the Euler Characteristic. These techniques can be further extended to higher dimensional QFTs or different topological invariants. 1
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Counting operators in Effective Field Theories
Dujava, Jonáš ; Vaško, Petr (advisor) ; Susič, Vasja (referee)
When applying physical calculations to the real world, it is always necessary to make some approximations. In the context of field theories, in particular the quantum field theories used in particle physics, a systematic treatment of this problem is provided by the framework of Effective Field Theories. Working in a given energy range, it is enough to consider only a couple of particles, while the existence of the rest only contributes some corrections. This is reflected in the structure of Effective Field Theory Lagrangians given as perturbation series, which are in general composed of all possible operators consistent with locality, unitarity, and symmetry assumptions. Obviously, it is advantageous to work with a minimal set of operators covering all physical phenomena, however the construction of the operator basis is very hard in general. Simpler step is to at least count all independent operators with a given number of derivatives and particle fields. To this end, the generating function (termed the Hilbert series) is introduced, with coefficients precisely being the number of independent operators of a given type. One can consider only scalar operators, that is Lorentz and gauge invariant operators, moreover consistent with other additional symmetries. To count independent operators it is furthermore...
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Optimization of Integration of Promax Training Equipment into Education
Vaško, Petr ; Číka, Petr (referee) ; Škorpil, Vladislav (advisor)
This thesis is focused on familiarization with the instructional device PROMAX, which is an illustrative example of functioning of a private central telephone switchboard, including simulation of the interconnection with the central telephone switchboard. First, the completion including wiring was carried out, the followed by the initial enlivening of the laboratory equipment, and detailed familiarization with its basic functions. After obtaining the requisite knowledge of the device, a comprehensible manual with individual parts of the tutorial system described in detail was elaborated. The emphasis is placed on understanding the problems of functions of individual blocks of the telephone switchboard, the successive modules, and the principle of interconnection. In the following part of the thesis a design of the laboratory tasks for students is carried out. They are designed to practical verification of the performance of the individual blocks, their interconnection and configuration. The attachments which are a part of the thesis contain the model design of the individual laboratory tasks.
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