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Title: Nombres $p$-àdics i aplicacions en física i topologia
Author: Ferré Moragues, Andreu
Director/Tutor: Travesa i Grau, Artur
Keywords: Nombres p-àdics
Treballs de fi de grau
Partícules (Física nuclear)
p-adic numbers
Bachelor's thesis
Particles (Nuclear physics)
Issue Date: 30-Jun-2015
Abstract: In this undergraduate thesis we begin by introducing the $p$-adic numbers and their basic properties, as well as the adeles. We then give an application to particle physics, using adeles extensively, to regularize divergent products through a product formula thereby endowing them of precise meaning. Next we discuss the topological differences between p-adic numbers and real numbers, and show some kind of euclidean models for them. This will prove helpful in the last chapter, where we will prove an equivalence of topological conjectures, which has been one of the goals of the project. Finally, we give a general approach to how the proof by Pardon [17] of the 3-dimensional case of this conjecture, which uses this equivalence, is carried out.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Artur Travesa i Grau
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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