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Meu Titulo Aqui Novamente? alexandre hefren de vasconcelos júnior ASPECTOSESTRUTURAISDACORRENTE ELETROMAGNÉTICADEPORTADORESDECARGA ELÉTRICACOMSPIN- 1 ASPECTOSESTRUTURAISDACORRENTEELETROMAGNÉTICA DEPORTADORESDECARGAELÉTRICACOMSPIN- 1 alexandre hefren de vasconcelos júnior Dissertação de Mestrado Julho 2016 Alexandre Hefren de Vasconcelos Júnior. Aspectos Estruturais da Cor- rente Eletromagnética de Portadores de Carga Elétrica com Spin-1. Disser- tação de Mestrado, Título de Mestre. © Julho 2016 supervisors: José Abdalla Helayël-Neto - Orientador Rio de Janeiro Julho 2016 “As long as we have what we have inside -the capacity to love, to work, to hear music,to see a flower, to look at the world as it is -nothing can stop us from being happy. But one thing you must take seriously. You must get rid of the ifs of life. Many people tell you,“I would be happy -if I had a certain job,or if I were better looking,or if a certain person would marry me”.There isn’t any such thing. You must live your life unconditionally, without the ifs”. (Arthur Rubinstein) Aos que amo. RESUMO Esta Dissertação versa sobre uma discussão em torno da relação entre spin, carga elétrica, massa e extensibilidade de partículas ele- mentares. Trata-se de um estudo que busca destacar esses pontos fundamentais através, principalmente, da interação eletromagnética e elucubrar reflexões no âmbito das propriedades de partículas ele- mentares. A importância do spin se revela à medida que investigamos as ques- tões aqui propostas. Em particular, faz-se uma análise comparativa da estrutura da corrente eletromagnética de partículas elementares de naturezas fermiônica e bosônica. Destaca-se especialmente o caso bosônico cujos portadores de carga são spin-1, representados pelos bósons-W do setor eletrofraco do Modelo Padrão. ABSTRACT This Dissertation discusses the relation between spin, electric charge, mass and extensibility of truly elementary particles from the point of view of the electromagnetic interactions at a semi-classical level. The importance of spin in the framework of classical electrodyna- mics becomes evident throughout the investigation of a number of issues worked out in this contribution. In particular, we carry out a comparative analysis of the structure of the electromagnetic current for elementary particles of both bosonic and fermionic natures. Spe- cial emphasis is placed on the case of spin-1 charge carriers, more specifically, the W-bosons of the electroweak sector of the Standard Model. vii “Of course there is no formula for success except perhaps an unconditional acceptance of life and what it brings” (Arthur Rubinstein) AGRADECIMENTOS Após dois anos de trabalho, estou completando o mestrado. Con- forme dito na minha monografia de graduação, um de meus objetivos foi, e será, diminuir minha própria ignorância. Porém, não é possível avançar sem as ajudas indubitavelmente necessárias recebidas de di- versas pessoas ao longo da vida. Por isso, quero aqui registrar meus sinceros e lídimos agradecimentos. Agradeço ao Professor Helayël, meu orientador, por ter me aten- dido desde 2012, quando o conheci no CBPF, e me orientado de 2014 até o presente momento, que marca o fim do mestrado. E se cheguei ao CBPF, foi também por ser orientado na graduação pelo Professor Carlos Alberto, a quem agradeço pelos valiosos conselhos. Agradeço a todos Professores que discutiram Física comigo. Ao Professor Sebastião pela ajuda dada, ao Professor Bert Schroer pe- las explicações, discussões e referências dadas, ao Professor Nami também pelas conversas sobre Física. Ao professor Ramos, por con- tinuar sendo atencioso comigo. A todos professores que me deram boas aulas. Aos professores das disciplinas básicas; Fernando, Shel- lard e Evaldo com seu bom humor. A todos meus amigos. Especialmente, aos que dividiram a sala 514-D comigo; Guilherme, Rafael, Ricardo, Lucho, Juan e também Dr.Noguera, que, mesmo não sendo da sala, estava sempre fazendo visitas. Agradeço ao meu pai e à minha mãe, que entendem e apoiam o caminho que tomei. Ao padrinho Egídio e à madrinha Luiciene pela contínua ajuda e atenção que tornaram meu caminho acadêmico me- nos árduo. À minha tia Heloísa pela preocupação comigo. À minha irmã. A meus avós pelo carinho. Agradeço a todos que contribuíram na conclusão dessa etapa. Ao CNPq, pelo financiamento da bolsa de mestrado. ix SUMÁRIO i apresentação geral1 1 introdução3 ii discussão9 2 spin 11 2.1 Datação Histórica 11 2.2 O Conceito de Spin 14 2.3 Momento Magnético 20 2.3.1 Momento Magnético Anômalo 25 2.4 Momento de Dipolo Elétrico do Elétron 28 2.5 Wigner e a Classificação do Spin 30 2.6 Quiralidade e Helicidade 35 3 os spins 0 e 1=2 39 3.1 Klein-Gordon e Schrödinger 42 3.2 Dirac e Pauli 45 3.3 Zitterbewung 49 3.3.1 Transformação de Foldy-Wouthuysen 52 3.4 Equações de Maxwell - Caso Fermiônico 54 3.5 Fatores de Forma e Corrente Fermiônica 57 3.6 Campo Clássico Estendido 60 4 o spin 1 67 4.1 Polarizações 68 4.2 Caso Livre 71 4.3 Caso Interagente 73 4.4 Fator Giromagnético 75 4.5 Lagrangeana 79 4.6 Fator Giromagnético Corrigido 80 4.7 Acoplamento não Mínimo da Teoria Eletrofraca 82 4.7.1 A Relação com o Higgs 85 4.8 Equações de Maxwell - Caso Bosônico 88 4.9 Decomposição de Gordon e Autointeração 94 4.10 Campo Clássico Estendido 94 5 spin, carga e massa 99 5.1 Teoria Quântica de Campos e Mecânica Quântica 99 5.2 Partícula e Localização 101 5.2.1 Localização 101 5.2.2 Partícula 107 5.3 Conservação e Superseleção 109 5.4 O Fator Giromagnético 114 6 comentários finais 119 xi xii sumário iii apêndice 123 a apêndice 125 a.1 Correntes Eletromagnéticas 125 referências bibliográficas 127 LISTADEFIGURAS Figura 1 Esquema vetorial 22 Figura 2 Precessão do momento angular(clássico) 23 Figura 3 Precessão do momento angular(clássico) 24 Figura 4 Níveis de energia do geonium para elétron. Da esquerda para direita: os níveis de ener- gia de cyclotron,do spin, das oscilações axiais e do movimento magnetron. Quando !s = !c, !a = 0 implica em degenerescências. 24 Figura 5 Experimento de Penning Trap 25 Figura 6 Diagramas de Feynman 64 Figura 7 Partículas elementares 108 LISTADETABELAS Tabela 1 Fatores giromagnéticos (g) de algumas partí- culas. [41][42][43][44][45] 26 Tabela 2 Transformações sob CPT. 29 Tabela 3 Correntes Eletromagnéticas 125 xiii Parte I APRESENTAÇÃOGERAL INTRODUÇÃO 1 A interação eletromagnética nos fornece a possibilidade de testar muito do que as teorias formulam, isto é, possui fundamental impor- tância na formulação das teorias físicas. É um fato histórico que o eletromagnetismo serviu, e ainda serve, de modelo teórico e foi área de importantíssimas descobertas na Física. Ela é a interação predo- minante em um grande intervalo de escalas espaciais, especialmente nas escalas da vida, isto é, nas dimensões espaciais em que a vida se desenvolve. Graças a isso, ela nos permite experimentar a Natureza e criar intuição física diretamente na nossa escala “habitat”. Evidente- mente, a Física já conhece, teoricamente, o intervalo de 10-35m (Com- primento de Plank) a 1026m (Raio do Universo visível), enquanto a vida tal qual conhecemos só ocupa em torno de dez ordens de gran- deza. Porém, a interação eletromagnética não é confinada, ao con- trário da fraca e da forte[1][2][3][4], e está por trás das medidadas experimentais que obtemos em laboratórios. Por uma questão observacional, foi a carga elétrica que primeiro revelou seus efeitos para a humanidade. O spin [5] só foi descoberto depois e nasceu ao longo da construção da mecânica quântica, mas conseguiu receber notória atenção à medida que o entendimento da Física evoluia. Hoje, sabemos que alguns efeitos de spin são mais fracos, no sentido da detecção experimental, mas existem e abrem caminho para novas descobertas. O conceito de spin de partículas elementares já existe há mais de noventa anos, porém é um assunto atual, pois não chegamos ainda ao conhecimento final que descreva satisfatoriamente como o spin surge, atua, relacionana-se com a estrutura do espaço-tempo e promove con- sequências nas caracterizações das interações fundamentais. Ao invertigarmos a natureza do spin, considerado como uma pro- priedade da matéria, seja bosônica ou fermiônica, percebemos a ne- cessidade de entender conceitos fundamentais que carecem de uma explicação universal e realmente elucidadora. Embora trabalhemos com partículas fundamentais, portadoras de propriedades físicas, não conhecemos com precisão o que é uma partícula elementar. Pode-se dizer que esse aludido nível de entendimento que busca o presente autor é meramente acadêmico e não vivifica contribuição concreta para a Física. Entretanto, a posição do autor é que já não se pode mais extrair resultados fundamentais como os muitos obtidos ao longo da história da Física devido a uma falta de entendimento da estrutura mais fundamental que forma a Física. É possível sim avançar com os olhos fechados em alguns trechos da Ciência, mas, em alguma hora, 3 4 introdução se faz necessário repensar o caminho que tomamos, as bases que vão nos direcionar ao maior entendimento dos conhecimentos que a Na- tureza nos permite conhecer. Sabemos que o conceito de campo surgiu com certa naturalidade no caminho que a Física tomou para descerever partículas, conside- radas inicialmente como elementos mais importantes de uma teoria que busque entender um Todo a partir das suas partes. Embora não exista sempre uma bijeção entre campo associado e partícula de inte- resse [6], foi possível inserir os graus de liberdade de uma partícula nos de um campo, mesmo pagando, em teoria de gauge, o preço de espúrios graus de liberdade que acompanham a teoria. É assaz notório o sucesso que teoria de campos conquistou com o trabalho de enorme esforço de inúmeros físicos ao longo da história[7], especialmente através da teoria quântica de campos.
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