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Linked Open Data
$p$-adic groups in quantum mechanics
Identificadores del recurso
http://hdl.handle.net/2445/186255
Procedencia
(Dipòsit Digital de la Universitat de Barcelona)

Ficha

Título:
$p$-adic groups in quantum mechanics
Tema:
Nombres p-àdics
Camps p-àdics
Anàlisi p-àdica
Teoria quàntica
Treballs de fi de grau
p-adic numbers
p-adic fields
p-adic analysis
Quantum theory
Bachelor's theses
Descrición:
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Artur Travesa i Grau
[en] Number theory is being used in physics as a mathematical tool more and more. At the end of the 20th century, $p$-adic numbers made its appearance in quantum gravitational theories like string theory. This was motivated by the non-archimedian nature of space time at Planck scale. In this work we aim to formalize the basis of $p$-adic physics by exploring how to translate complex Quantum Mechanics to $p$-adic Quantum mechanics. This will be done using Weyl's formalism, which defines bounded operators and allows to relate different time-evolution pictures in quantum mechanics. This is done by the means of representation theory. We will be exploring the representation theory of $p$-adic reductive groups, specially induced, supercuspidal and projective representations. With that knowledge we will define the $p$-adic Heisenberg group that encodes the information on the $p$-adic phase space and study the Schrödinger representation. We will explain the importance of the Stone-von Neumann theorem that states uniqueness up to equivalence and we will study the Maslov indices of the group.
Fonte:
Treballs Finals de Grau (TFG) - Matemàtiques
Idioma:
English
Autor/Productor:
Blanco Cabanillas, Anna
Otros colaboradores/productores:
Travesa i Grau, Artur
Dereitos:
cc-by-nc-nd (c) Anna Blanco Cabanillas, 2022
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
Data:
2022-06-02T10:06:29Z
2022-01-22
Tipo de recurso:
info:eu-repo/semantics/bachelorThesis
Formato:
49 p.
application/pdf

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    1. <dc:title>$p$-adic groups in quantum mechanics</dc:title>

    2. <dc:contributor.advisor>Travesa i Grau, Artur</dc:contributor.advisor>

    3. <dc:creator>Blanco Cabanillas, Anna</dc:creator>

    4. <dc:subject.classification>Nombres p-àdics</dc:subject.classification>

    5. <dc:subject.classification>Camps p-àdics</dc:subject.classification>

    6. <dc:subject.classification>Anàlisi p-àdica</dc:subject.classification>

    7. <dc:subject.classification>Teoria quàntica</dc:subject.classification>

    8. <dc:subject.classification>Treballs de fi de grau</dc:subject.classification>

    9. <dc:subject.other>p-adic numbers</dc:subject.other>

    10. <dc:subject.other>p-adic fields</dc:subject.other>

    11. <dc:subject.other>p-adic analysis</dc:subject.other>

    12. <dc:subject.other>Quantum theory</dc:subject.other>

    13. <dc:subject.other>Bachelor's theses</dc:subject.other>

    14. <dcterms:abstract>[en] Number theory is being used in physics as a mathematical tool more and more. At the end of the 20th century, $p$-adic numbers made its appearance in quantum gravitational theories like string theory. This was motivated by the non-archimedian nature of space time at Planck scale. In this work we aim to formalize the basis of $p$-adic physics by exploring how to translate complex Quantum Mechanics to $p$-adic Quantum mechanics. This will be done using Weyl's formalism, which defines bounded operators and allows to relate different time-evolution pictures in quantum mechanics. This is done by the means of representation theory. We will be exploring the representation theory of $p$-adic reductive groups, specially induced, supercuspidal and projective representations. With that knowledge we will define the $p$-adic Heisenberg group that encodes the information on the $p$-adic phase space and study the Schrödinger representation. We will explain the importance of the Stone-von Neumann theorem that states uniqueness up to equivalence and we will study the Maslov indices of the group.</dcterms:abstract>

    15. <dcterms:dateAccepted>2022-06-02T10:06:29Z</dcterms:dateAccepted>

    16. <dcterms:available>2022-06-02T10:06:29Z</dcterms:available>

    17. <dcterms:created>2022-06-02T10:06:29Z</dcterms:created>

    18. <dcterms:issued>2022-01-22</dcterms:issued>

    19. <dc:type>info:eu-repo/semantics/bachelorThesis</dc:type>

    20. <dc:identifier>http://hdl.handle.net/2445/186255</dc:identifier>

    21. <dc:language>eng</dc:language>

    22. <dc:rights>http://creativecommons.org/licenses/by-nc-nd/3.0/es/</dc:rights>

    23. <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>

    24. <dc:rights>cc-by-nc-nd (c) Anna Blanco Cabanillas, 2022</dc:rights>

    25. <dc:source>Treballs Finals de Grau (TFG) - Matemàtiques</dc:source>

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      1. <dc:title>$p$-adic groups in quantum mechanics</dc:title>

      2. <dc:creator>Blanco Cabanillas, Anna</dc:creator>

      3. <dc:contributor>Travesa i Grau, Artur</dc:contributor>

      4. <dc:description>Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Artur Travesa i Grau</dc:description>

      5. <dc:description>[en] Number theory is being used in physics as a mathematical tool more and more. At the end of the 20th century, $p$-adic numbers made its appearance in quantum gravitational theories like string theory. This was motivated by the non-archimedian nature of space time at Planck scale. In this work we aim to formalize the basis of $p$-adic physics by exploring how to translate complex Quantum Mechanics to $p$-adic Quantum mechanics. This will be done using Weyl's formalism, which defines bounded operators and allows to relate different time-evolution pictures in quantum mechanics. This is done by the means of representation theory. We will be exploring the representation theory of $p$-adic reductive groups, specially induced, supercuspidal and projective representations. With that knowledge we will define the $p$-adic Heisenberg group that encodes the information on the $p$-adic phase space and study the Schrödinger representation. We will explain the importance of the Stone-von Neumann theorem that states uniqueness up to equivalence and we will study the Maslov indices of the group.</dc:description>

      6. <dc:date>2022-06-02T10:06:29Z</dc:date>

      7. <dc:date>2022-06-02T10:06:29Z</dc:date>

      8. <dc:date>2022-01-22</dc:date>

      9. <dc:type>info:eu-repo/semantics/bachelorThesis</dc:type>

      10. <dc:identifier>http://hdl.handle.net/2445/186255</dc:identifier>

      11. <dc:language>eng</dc:language>

      12. <dc:rights>http://creativecommons.org/licenses/by-nc-nd/3.0/es/</dc:rights>

      13. <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>

      14. <dc:rights>cc-by-nc-nd (c) Anna Blanco Cabanillas, 2022</dc:rights>

      15. <dc:source>Treballs Finals de Grau (TFG) - Matemàtiques</dc:source>

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