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z2I*jh5Zk7MTDQvMxyrG!Dj>*gmoVwepeWb@Gn-dWEd2 diff --git a/pres4.tex b/pres4.tex index 49e8b17..cfe1d20 100644 --- a/pres4.tex +++ b/pres4.tex @@ -510,31 +510,102 @@ \end{itemize} \end{frame} -\begin{frame} +\begin{frame}{Invariancia de norma} + \begin{itemize} + \item Todas las fuerzas pueden expresarse como teorías de norma + \item Son invariantes ante la transformación de norma + \item La conservación de carga (conservación aditiva) es invariante ante una transformación global + \item AL agregar la dependencia para una carga no estática se mantiene la invariancia incluso en transformación local. + \end{itemize} +\end{frame} + +\begin{frame}{Invariancia de norma - Grados de libertad} + \begin{itemize} + \item Libertad parcial de elegir el potencial electromagnético + \item Parecía una teoría con cabos sueltos, o sólo una peculiaridad matemática + \item La invariancia de norma dicta la forma d ela interacción y los campos vectoriales sin masa. + \end{itemize} +\end{frame} + +\begin{frame}{Potenciales vectoriales y normas covariantes} + $(A_0,\mathbf{A})$ + \begin{align} + D_{\mu}=& (D_0,\mathbf{D})\\ + D_0 =& \frac{1}{c}\frac{\partial}{\partial t} + \frac{iqA_0}{\hbar c}\\ + \mathbf{D} =& \nabla - \frac{iq\mathbf{A}}{\hbar c} + \end{align} +\end{frame} + +\begin{frame}{Movimiento de los campos vectoriales} + \begin{align*} + \frac{1}{c^2}\frac{\partial^2 A_0}{\partial t^2} -\nabla A_0 =& \rho = \psi^* q \psi \\ + \frac{1}{c^2}\frac{\partial^2 A_i}{\partial t^2} -\nabla A_i =& \frac{j_i}{c} = \psi^* \frac{q\vec{v}_i}{c} \psi + \end{align*} + Con la condición para su invariancia de norma: \begin{equation} - \begin{pmatrix} - d' \\ - s' \\ - b' - \end{pmatrix} = - \begin{pmatrix} - V_{ud} & V_{us} & V_{ub} \\ - V_{cd} & V_{cs} & V_{cb} \\ - V_{td} & V_{ts} & V_{tb} - \end{pmatrix} - \begin{pmatrix} - d \\ - s \\ - b - \end{pmatrix} + \frac{1}{c^2}\frac{\partial^2\epsilon(\vec{x},t)}{\partial t^2} - \nabla^2 \epsilon(\vec{x},t) = 0 \end{equation} \end{frame} +\begin{frame}{Bosones sin masa} + \begin{itemize} + \item Aparece la necesidad de que los bosones de norma no tengan masa + \item La invariancia local se extiende a la global + \item La fase en una función de onda es arbitraria + \item Pero siempre debe ser la misma fase en todos los puntos del espacio tiempo. + \end{itemize} +\end{frame} +\begin{frame}{Sentido físico de los potenciales vectoriales} + \begin{itemize} + \item Aparece en la teoría cuántica + \end{itemize} + + En ausencia de campo electromagnético, la ecuación estacionaria de Schrödinger: + \begin{equation} + -\frac{\hbar^2}{2m}\nabla^2 \psi_0 = E\psi_0, + \end{equation} +\end{frame} +\begin{frame}{Ecuación de Schrödinger con campo vectorial electromagnético estático} + \begin{equation} + -\frac{\hbar^2}{2m}\mathbf{D}^2\psi= -\frac{\hbar^2}{2m} \left( \nabla + \frac{ie\mathbf{A}(\vec{x})}{\hbar c}\right)^2 \psi + \end{equation} + \begin{figure}[ht!] + \begin{center} + \includegraphics[width=0.5\linewidth]{bohm_aharanov.jpg} + \caption{Imagen del experomento de Aharanov-Bohm. Imagen con licencia CC-BY-SA toma de wikipedia} + \label{fig:bohm} + \end{center} + \end{figure} +\end{frame} +\begin{frame}{Invariancia de norma y teorías no abelianas} + \begin{itemize} + \item La invariancia pide campos vectoriales sin masa + \item Bosones de interacción débil con masa y cargados + \item Bosones de interacción fuerte sin masa, pero cargados + \item Problemas por ejemplo en teoría de perturbaciones + \end{itemize} +\end{frame} +\begin{frame}{Mecanismo de Higgs} + \begin{itemize} + \item Rompimiento de simetría aproximada + \item Rompimiento de simetría espontáneo + \item Simetrías escondidas por ejemplo en los ferromagnetos + \end{itemize} +\end{frame} - +\begin{frame}{Bosón de Higgs} + \begin{itemize} + \item Campo escalar complejo invariante de norma, $\phi$ y $\phi^*$ + \item Representan mesones escalares $H^+$ y $H^-$ + \begin{equation*} + \phi = \frac{1}{\sqrt{2}}(\phi_1 + i \phi_2) + \end{equation*} + \item Obedecen a la ecuación de Klein-Gordon + \end{itemize} +\end{frame} \end{document} diff --git a/tarea2.pdf b/tarea2.pdf index c01523b3fa560baac8e6ad2062c8880e11918ac4..2989f07a217da75320b1e94b740d448c7c70d8c2 100644 GIT binary patch delta 103 zcmaDpk@fjR)`l&N6?V+V7KYQS?HCn6jP3L67`Zu}T^-F`+zd>d%p48PolG4~j7-dp b4V)c~EsPD#ES)W!>=bMWDVhGpo$)sSw$>X? delta 103 zcmaDpk@fjR)`l&N6?V)9rbg4N?HCn6jP3L67`Zu}E!>=)-P|n9OfB3joeT}#Ok9o3 b4P2aDTrHf;om`#W>=bMWDVhGpo$)sS)e0O!

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