Catalònica: Agregador de continguts digitals de Catalunya

Està a:  › Dades de registre

$p$-adic groups in quantum mechanics

Identificadors del recurs

http://hdl.handle.net/2445/186255

Procedència

(Dipòsit Digital de la Universitat de Barcelona)

Fitxa

Títol:: $p$-adic groups in quantum mechanics
Matèria:: 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
Descripció:: 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.
Font:: Treballs Finals de Grau (TFG) - Matemàtiques
Idioma:: English
Autor/Productor:: Blanco Cabanillas, Anna
Altres col·laboradors/productors:: Travesa i Grau, Artur
Drets:: 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
Tipus de recurs:: info:eu-repo/semantics/bachelorThesis
Format:: 49 p.; application/pdf

oai_dc

Descarregar XML

<?xml version="1.0" encoding="UTF-8" ?>

< oai_dc:dc schemaLocation =" http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd " >
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:subject > Nombres p-àdics </ dc:subject >
5. < dc:subject > Camps p-àdics </ dc:subject >
6. < dc:subject > Anàlisi p-àdica </ dc:subject >
7. < dc:subject > Teoria quàntica </ dc:subject >
8. < dc:subject > Treballs de fi de grau </ dc:subject >
9. < dc:subject > p-adic numbers </ dc:subject >
10. < dc:subject > p-adic fields </ dc:subject >
11. < dc:subject > p-adic analysis </ dc:subject >
12. < dc:subject > Quantum theory </ dc:subject >
13. < dc:subject > Bachelor's theses </ dc:subject >
14. < dc:description > Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Artur Travesa i Grau </ dc:description >
15. < 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 >
16. < dc:date > 2022-06-02T10:06:29Z </ dc:date >
17. < dc:date > 2022-06-02T10:06:29Z </ dc:date >
18. < dc:date > 2022-01-22 </ dc:date >
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 > cc-by-nc-nd (c) Anna Blanco Cabanillas, 2022 </ dc:rights >
23. < dc:rights > http://creativecommons.org/licenses/by-nc-nd/3.0/es/ </ dc:rights >
24. < dc:rights > info:eu-repo/semantics/openAccess </ dc:rights >
25. < dc:format > 49 p. </ dc:format >
26. < dc:format > application/pdf </ dc:format >
27. < dc:source > Treballs Finals de Grau (TFG) - Matemàtiques </ dc:source >
</ oai_dc:dc >

edm

Descarregar XML

<?xml version="1.0" encoding="UTF-8" ?>

< rdf:RDF schemaLocation =" http://www.w3.org/1999/02/22-rdf-syntax-ns# http://www.europeana.eu/schemas/edm/EDM.xsd " >
1. < edm:ProvidedCHO about =" https://catalonica.bnc.cat/catalonicahub/lod/oai:diposit.ub.edu:2445_--_186255#ent0 " >
  1. < dc:contributor > Travesa i Grau, Artur </ dc:contributor >
  2. < dc:creator > Blanco Cabanillas, Anna </ dc:creator >
  3. < dc:date > 2022-06-02T10:06:29Z </ dc:date >
  4. < dc:date > 2022-06-02T10:06:29Z </ dc:date >
  5. < dc:date > 2022-01-22 </ dc:date >
  6. < dc:description > Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Artur Travesa i Grau </ dc:description >
  7. < 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 >
  8. < dc:identifier > http://hdl.handle.net/2445/186255 </ dc:identifier >
  9. < dc:language > eng </ dc:language >
  10. < dc:rights > cc-by-nc-nd (c) Anna Blanco Cabanillas, 2022 </ dc:rights >
  11. < dc:rights > http://creativecommons.org/licenses/by-nc-nd/3.0/es/ </ dc:rights >
  12. < dc:rights > info:eu-repo/semantics/openAccess </ dc:rights >
  13. < dc:source > Treballs Finals de Grau (TFG) - Matemàtiques </ dc:source >
  14. < dc:subject > Nombres p-àdics </ dc:subject >
  15. < dc:subject > Camps p-àdics </ dc:subject >
  16. < dc:subject > Anàlisi p-àdica </ dc:subject >
  17. < dc:subject > Teoria quàntica </ dc:subject >
  18. < dc:subject > Treballs de fi de grau </ dc:subject >
  19. < dc:subject > p-adic numbers </ dc:subject >
  20. < dc:subject > p-adic fields </ dc:subject >
  21. < dc:subject > p-adic analysis </ dc:subject >
  22. < dc:subject > Quantum theory </ dc:subject >
  23. < dc:subject > Bachelor's theses </ dc:subject >
  24. < dc:title > $p$-adic groups in quantum mechanics </ dc:title >
  25. < dc:type > info:eu-repo/semantics/bachelorThesis </ dc:type >
  26. < edm:type > TEXT </ edm:type >
  </ edm:ProvidedCHO >
2. < ore:Aggregation about =" https://catalonica.bnc.cat/catalonicahub/lod/oai:diposit.ub.edu:2445_--_186255#ent1 " >
  1. < edm:aggregatedCHO resource =" https://catalonica.bnc.cat/catalonicahub/lod/oai:diposit.ub.edu:2445_--_186255#ent0 " />
  2. < edm:dataProvider > Dipòsit Digital de la Universitat de Barcelona </ edm:dataProvider >
  3. < edm:isShownAt resource =" http://hdl.handle.net/2445/186255 " />
  4. < edm:isShownBy resource =" http://diposit.ub.edu/dspace/bitstream/2445/186255/1/ces186255.pdf " />
  5. < edm:provider > Catalònica </ edm:provider >
  6. < edm:rights resource =" http://creativecommons.org/licenses/by-nc-nd/3.0/es/ " />
  </ ore:Aggregation >
</ rdf:RDF >

marc

Descarregar XML

<?xml version="1.0" encoding="UTF-8" ?>

< record schemaLocation =" http://www.loc.gov/MARC21/slim http://www.loc.gov/standards/marcxml/schema/MARC21slim.xsd " >
1. < leader > 00925njm 22002777a 4500 </ leader >
2. < datafield ind1 =" " ind2 =" " tag =" 042 " >
  1. < subfield code =" a " > dc </ subfield >
  </ datafield >
3. < datafield ind1 =" " ind2 =" " tag =" 720 " >
  1. < subfield code =" a " > Blanco Cabanillas, Anna </ subfield >
  2. < subfield code =" e " > author </ subfield >
  </ datafield >
4. < datafield ind1 =" " ind2 =" " tag =" 260 " >
  1. < subfield code =" c " > 2022-01-22 </ subfield >
  </ datafield >
5. < datafield ind1 =" " ind2 =" " tag =" 520 " >
  1. < subfield code =" a " > [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. </ subfield >
  </ datafield >
6. < datafield ind1 =" 8 " ind2 =" " tag =" 024 " >
  1. < subfield code =" a " > http://hdl.handle.net/2445/186255 </ subfield >
  </ datafield >
7. < datafield ind1 =" 0 " ind2 =" 0 " tag =" 245 " >
  1. < subfield code =" a " > $p$-adic groups in quantum mechanics </ subfield >
  </ datafield >
</ record >

mets

Descarregar XML

<?xml version="1.0" encoding="UTF-8" ?>

< mets ID =" DSpace_ITEM_2445-186255 " OBJID =" hdl:2445/186255 " PROFILE =" DSpace METS SIP Profile 1.0 " TYPE =" DSpace ITEM " schemaLocation =" http://www.loc.gov/METS/ http://www.loc.gov/standards/mets/mets.xsd " >
1. < metsHdr CREATEDATE =" 2024-06-06T04:46:33Z " >
  1. < agent ROLE =" CUSTODIAN " TYPE =" ORGANIZATION " >
    1. < name > Dipòsit Digital de la Universitat de Barcelona </ name >
    </ agent >
  </ metsHdr >
2. < dmdSec ID =" DMD_2445_186255 " >
  1. < mdWrap MDTYPE =" MODS " >
    1. < xmlData schemaLocation =" http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-1.xsd " >
      1. < mods:mods schemaLocation =" http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-1.xsd " >
        
        < mods:name >
        
        < mods:role >
        
        < mods:roleTerm type =" text " > advisor </ mods:roleTerm >
        
        </ mods:role >
        
        < mods:namePart > Travesa i Grau, Artur </ mods:namePart >
        
        </ mods:name >
        
        < mods:name >
        
        < mods:role >
        
        < mods:roleTerm type =" text " > author </ mods:roleTerm >
        
        </ mods:role >
        
        < mods:namePart > Blanco Cabanillas, Anna </ mods:namePart >
        
        </ mods:name >
        
        < mods:extension >
        
        < mods:dateAccessioned encoding =" iso8601 " > 2022-06-02T10:06:29Z </ mods:dateAccessioned >
        
        </ mods:extension >
        
        < mods:extension >
        
        < mods:dateAvailable encoding =" iso8601 " > 2022-06-02T10:06:29Z </ mods:dateAvailable >
        
        </ mods:extension >
        
        < mods:originInfo >
        
        < mods:dateIssued encoding =" iso8601 " > 2022-01-22 </ mods:dateIssued >
        
        </ mods:originInfo >
        
        < mods:identifier type =" uri " > http://hdl.handle.net/2445/186255 </ mods:identifier >
        
        < mods: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. </ mods:abstract >
        
        < mods:language >
        
        < mods:languageTerm authority =" rfc3066 " > eng </ mods:languageTerm >
        
        </ mods:language >
        
        < mods:accessCondition type =" useAndReproduction " > cc-by-nc-nd (c) Anna Blanco Cabanillas, 2022 </ mods:accessCondition >
        
        < mods:titleInfo >
        
        < mods:title > $p$-adic groups in quantum mechanics </ mods:title >
        
        </ mods:titleInfo >
        
        < mods:genre > info:eu-repo/semantics/bachelorThesis </ mods:genre >
        
        </ mods:mods >
      </ xmlData >
    </ mdWrap >
  </ dmdSec >
3. < amdSec ID =" TMD_2445_186255 " >
  1. < rightsMD ID =" RIG_2445_186255 " >
    1. < mdWrap MDTYPE =" OTHER " MIMETYPE =" text/plain " OTHERMDTYPE =" DSpaceDepositLicense " >
      1. < binData > RWxzIG1hdGVyaWFscyBsbGl1cmF0cyBhbCBEaXDDsnNpdCBkaWdpdGFsIGRlIGxhIFVCIHF1ZSBlc3RpZ3VpbiBzdWJqZWN0ZXMgYSB1bmEgbGxpY8OobmNpYSBkZSBDcmVhdGl2ZSBDb21tb25zLAplbiBlbCBtb21lbnQgZGUgbGxpdXJhciBlbCBkb2N1bWVudCwgZWwgcHJvcGkgdXN1YXJpIGwnaGEgZCdlc2NvbGxpci4KU2kgdXMgcGxhdSBubyBvYmxpZGV1IGFzc2lnbmFyIHVuYSBsbGljw6huY2lhIGFsIHZvc3RyZSBkb2N1bWVudCEuCg== </ binData >
      </ mdWrap >
    </ rightsMD >
  </ amdSec >
4. < amdSec ID =" FO_2445_186255_1 " >
  1. < techMD ID =" TECH_O_2445_186255_1 " >
    1. < mdWrap MDTYPE =" PREMIS " >
      1. < xmlData schemaLocation =" http://www.loc.gov/standards/premis http://www.loc.gov/standards/premis/PREMIS-v1-0.xsd " >
        
        < premis:premis >
        
        < premis:object >
        
        < premis:objectIdentifier >
        
        < premis:objectIdentifierType > URL </ premis:objectIdentifierType >
        
        < premis:objectIdentifierValue > http://diposit.ub.edu/dspace/bitstream/2445/186255/1/ces186255.pdf </ premis:objectIdentifierValue >
        
        </ premis:objectIdentifier >
        
        < premis:objectCategory > File </ premis:objectCategory >
        
        < premis:objectCharacteristics >
        
        < premis:fixity >
        
        < premis:messageDigestAlgorithm > MD5 </ premis:messageDigestAlgorithm >
        
        < premis:messageDigest > b2a25a7f4ad229ba7be48f01f4e71629 </ premis:messageDigest >
        
        </ premis:fixity >
        
        < premis:size > 309733 </ premis:size >
        
        < premis:format >
        
        < premis:formatDesignation >
        
        < premis:formatName > text/plain </ premis:formatName >
        
        </ premis:formatDesignation >
        
        </ premis:format >
        
        </ premis:objectCharacteristics >
        
        < premis:originalName > ces186255.pdf </ premis:originalName >
        
        </ premis:object >
        
        </ premis:premis >
        
        </ xmlData >
      </ mdWrap >
    </ techMD >
  </ amdSec >
5. < amdSec ID =" FO_2445_186255_2 " >
  1. < techMD ID =" TECH_O_2445_186255_2 " >
    1. < mdWrap MDTYPE =" PREMIS " >
      1. < xmlData schemaLocation =" http://www.loc.gov/standards/premis http://www.loc.gov/standards/premis/PREMIS-v1-0.xsd " >
        
        < premis:premis >
        
        < premis:object >
        
        < premis:objectIdentifier >
        
        < premis:objectIdentifierType > URL </ premis:objectIdentifierType >
        
        < premis:objectIdentifierValue > http://diposit.ub.edu/dspace/bitstream/2445/186255/2/tfg_blanco_cabanillas_anna.pdf </ premis:objectIdentifierValue >
        
        </ premis:objectIdentifier >
        
        < premis:objectCategory > File </ premis:objectCategory >
        
        < premis:objectCharacteristics >
        
        < premis:fixity >
        
        < premis:messageDigestAlgorithm > MD5 </ premis:messageDigestAlgorithm >
        
        < premis:messageDigest > d66115f85308672d824f502eb9c0c1dd </ premis:messageDigest >
        
        </ premis:fixity >
        
        < premis:size > 559245 </ premis:size >
        
        < premis:format >
        
        < premis:formatDesignation >
        
        < premis:formatName > application/pdf </ premis:formatName >
        
        </ premis:formatDesignation >
        
        </ premis:format >
        
        </ premis:objectCharacteristics >
        
        < premis:originalName > tfg_blanco_cabanillas_anna.pdf </ premis:originalName >
        
        </ premis:object >
        
        </ premis:premis >
        
        </ xmlData >
      </ mdWrap >
    </ techMD >
  </ amdSec >
6. < amdSec ID =" FT_2445_186255_5 " >
  1. < techMD ID =" TECH_T_2445_186255_5 " >
    1. < mdWrap MDTYPE =" PREMIS " >
      1. < xmlData schemaLocation =" http://www.loc.gov/standards/premis http://www.loc.gov/standards/premis/PREMIS-v1-0.xsd " >
        
        < premis:premis >
        
        < premis:object >
        
        < premis:objectIdentifier >
        
        < premis:objectIdentifierType > URL </ premis:objectIdentifierType >
        
        < premis:objectIdentifierValue > http://diposit.ub.edu/dspace/bitstream/2445/186255/5/tfg_blanco_cabanillas_anna.pdf.txt </ premis:objectIdentifierValue >
        
        </ premis:objectIdentifier >
        
        < premis:objectCategory > File </ premis:objectCategory >
        
        < premis:objectCharacteristics >
        
        < premis:fixity >
        
        < premis:messageDigestAlgorithm > MD5 </ premis:messageDigestAlgorithm >
        
        < premis:messageDigest > 6cc46f17bf7ad65cbe11755fd2850745 </ premis:messageDigest >
        
        </ premis:fixity >
        
        < premis:size > 104436 </ premis:size >
        
        < premis:format >
        
        < premis:formatDesignation >
        
        < premis:formatName > text/plain </ premis:formatName >
        
        </ premis:formatDesignation >
        
        </ premis:format >
        
        </ premis:objectCharacteristics >
        
        < premis:originalName > tfg_blanco_cabanillas_anna.pdf.txt </ premis:originalName >
        
        </ premis:object >
        
        </ premis:premis >
        
        </ xmlData >
      </ mdWrap >
    </ techMD >
  </ amdSec >
7. < fileSec >
  1. < fileGrp USE =" ORIGINAL " >
    1. < file ADMID =" FO_2445_186255_1 " CHECKSUM =" b2a25a7f4ad229ba7be48f01f4e71629 " CHECKSUMTYPE =" MD5 " GROUPID =" GROUP_BITSTREAM_2445_186255_1 " ID =" BITSTREAM_ORIGINAL_2445_186255_1 " MIMETYPE =" text/plain " SEQ =" 1 " SIZE =" 309733 " >
      1. < FLocat LOCTYPE =" URL " href =" http://diposit.ub.edu/dspace/bitstream/2445/186255/1/ces186255.pdf " type =" simple " />
      </ file >
    2. < file ADMID =" FO_2445_186255_2 " CHECKSUM =" d66115f85308672d824f502eb9c0c1dd " CHECKSUMTYPE =" MD5 " GROUPID =" GROUP_BITSTREAM_2445_186255_2 " ID =" BITSTREAM_ORIGINAL_2445_186255_2 " MIMETYPE =" application/pdf " SEQ =" 2 " SIZE =" 559245 " >
      1. < FLocat LOCTYPE =" URL " href =" http://diposit.ub.edu/dspace/bitstream/2445/186255/2/tfg_blanco_cabanillas_anna.pdf " type =" simple " />
      </ file >
    </ fileGrp >
  2. < fileGrp USE =" TEXT " >
    1. < file ADMID =" FT_2445_186255_5 " CHECKSUM =" 6cc46f17bf7ad65cbe11755fd2850745 " CHECKSUMTYPE =" MD5 " GROUPID =" GROUP_BITSTREAM_2445_186255_5 " ID =" BITSTREAM_TEXT_2445_186255_5 " MIMETYPE =" text/plain " SEQ =" 5 " SIZE =" 104436 " >
      1. < FLocat LOCTYPE =" URL " href =" http://diposit.ub.edu/dspace/bitstream/2445/186255/5/tfg_blanco_cabanillas_anna.pdf.txt " type =" simple " />
      </ file >
    </ fileGrp >
  </ fileSec >
8. < structMap LABEL =" DSpace Object " TYPE =" LOGICAL " >
  1. < div ADMID =" DMD_2445_186255 " TYPE =" DSpace Object Contents " >
    1. < div TYPE =" DSpace BITSTREAM " >
      1. < fptr FILEID =" BITSTREAM_ORIGINAL_2445_186255_1 " />
      </ div >
    2. < div TYPE =" DSpace BITSTREAM " >
      1. < fptr FILEID =" BITSTREAM_ORIGINAL_2445_186255_2 " />
      </ div >
    </ div >
  </ structMap >
</ mets >

mods

Descarregar XML

<?xml version="1.0" encoding="UTF-8" ?>

< mods:mods schemaLocation =" http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-1.xsd " >
1. < mods:name >
  1. < mods:namePart > Blanco Cabanillas, Anna </ mods:namePart >
  </ mods:name >
2. < mods:extension >
  1. < mods:dateAvailable encoding =" iso8601 " > 2022-06-02T10:06:29Z </ mods:dateAvailable >
  </ mods:extension >
3. < mods:extension >
  1. < mods:dateAccessioned encoding =" iso8601 " > 2022-06-02T10:06:29Z </ mods:dateAccessioned >
  </ mods:extension >
4. < mods:originInfo >
  1. < mods:dateIssued encoding =" iso8601 " > 2022-01-22 </ mods:dateIssued >
  </ mods:originInfo >
5. < mods:identifier type =" uri " > http://hdl.handle.net/2445/186255 </ mods:identifier >
6. < mods: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. </ mods:abstract >
7. < mods:language >
  1. < mods:languageTerm > eng </ mods:languageTerm >
  </ mods:language >
8. < mods:accessCondition type =" useAndReproduction " > http://creativecommons.org/licenses/by-nc-nd/3.0/es/ </ mods:accessCondition >
9. < mods:accessCondition type =" useAndReproduction " > info:eu-repo/semantics/openAccess </ mods:accessCondition >
10. < mods:accessCondition type =" useAndReproduction " > cc-by-nc-nd (c) Anna Blanco Cabanillas, 2022 </ mods:accessCondition >
11. < mods:titleInfo >
  1. < mods:title > $p$-adic groups in quantum mechanics </ mods:title >
  </ mods:titleInfo >
12. < mods:genre > info:eu-repo/semantics/bachelorThesis </ mods:genre >
</ mods:mods >

qdc

Descarregar XML

<?xml version="1.0" encoding="UTF-8" ?>

< qdc:qualifieddc schemaLocation =" http://purl.org/dc/elements/1.1/ http://dublincore.org/schemas/xmls/qdc/2006/01/06/dc.xsd http://purl.org/dc/terms/ http://dublincore.org/schemas/xmls/qdc/2006/01/06/dcterms.xsd http://dspace.org/qualifieddc/ http://www.ukoln.ac.uk/metadata/dcmi/xmlschema/qualifieddc.xsd " >
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 >
</ qdc:qualifieddc >

rdf

Descarregar XML

<?xml version="1.0" encoding="UTF-8" ?>

< rdf:RDF schemaLocation =" http://www.openarchives.org/OAI/2.0/rdf/ http://www.openarchives.org/OAI/2.0/rdf.xsd " >
1. < ow:Publication about =" oai:diposit.ub.edu:2445/186255 " >
  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 >
  </ ow:Publication >
</ rdf:RDF >

Biblioteca de Catalunya Carrer de l'Hospital, 56. 08001 Barcelona Adreça electrònica: catalonica@bnc.cat Tlf.: +34 932 702 300

Repositori OAI