Recent content by TAKEDA Hiroki

In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...

Thanks a lot. So Why is the (l.h.s) component ##(\partial W^i/\partial u)##, though (r.h.s.) component is ##(\partial W^i/\partial u)-(\partial K^i/\partial t)## ?? I want you to explain without using the projection ##\pi## because I'm not familiar with the bundle. In the following calculation...

Thank you for your reply! Nice to meet you, berkeman-san:smile:

Thank you for your reply. I see.. This equation is a definition rather than a derivation. But I have a question. This paper is written more precisely by using bundle than Hawking-Ellis Book(1973). In the book, they denote ##\partial\Psi_{(i)}(u,r)/\partial u)|_{u=0}## by ##\Delta\Psi_{(i)}##...

Hello everyone! I'm a graduate student in Japan. I'm studying Physics, especially Gravitational Waves , General Relativity, and Spacetime theory. I want to learn a lot and help another members. Nice meeting you.

In Hawking-Ellis Book(1973) "The large scale structure of space-time" p69-p70, they derive the energy-momentum tensor for perfect fluid by lagrangian formulation. They imply if ##D## is a sufficiently small compact region, one can represent a congruence by a diffeomorphism ##\gamma: [a,b]\times...