A sample prompt of what you can find in this page
Prompt by Demi444

You have to be symmetrical Stable Diffusion prompts

very few results

16 days ago

We consider the action $S_{\phi q}$ involving only $\phi_{\mu\nu}$ and quark fields $q(x)$ in general frames with Poincar\'e metric tensor $P_{\mu\nu}$: \be S_{\phi q} = \int (L_{\phi q} + L_{gf})d^4 x, \ee %%%%%%%%15%%%%22%%%%%24%%%22%%%19 \be L_{gf}=\frac{1}{2g^2}\e_{\a\b}\left[\p_\mu J^{\mu\a} - \frac{1}{2}\e^{\a\ld}\p_{\ld} J^\mu_\mu\right] \left[\p_\nu J^{\nu\b} - \frac{1}{2}\e^{\b\ld}\p_{\ld} J^\nu_\nu\right], \ee %%%%16%%%%%%%23%%%%%25%%%23%%%%20 where $L_{\phi q}$ is given in (7) with the $T(4)$ gauge curvature $C_{\mu\nu\a}$ given by (5). We have included a gauge-fixing term $L_{gf}$ specified by (20) involving ordinary partial derivative to break the $T(4)$ gauge symmetry so that the solution of gauge field equation is well-defined. The reason for including $L_{gf}$ is that field equations with gauge symmetry are known to be not well defined in general and that it is a nuisance to find explicit solutions of such field equations without having a gauge-fixing term. The quark fields play the source for producing a gravitational potential field $\phi_{\mu\nu}$. The $T(4)$ gravitational field equation for symmetric tensor field, $\phi_{\mu\nu}=\phi_{\nu\mu}$ can be derived from (19), \be H^{\mu\nu} + A^{\mu\nu}= \frac{g^2}{2} Sym \ \left[ \overline{q} i\G^\mu D^\nu q - i(D^\nu \overline{q}) \G^\mu q \right]\equiv g^2 T^{\mu\nu} , \ee %%%%%26%%%17%%%%%%%%%24%%%%%%26%%%24%21 $$ H^{\mu\nu} = Sym \left[D_\ld (J^{\ld}_\rho C^{\rho\mu\nu} - J^\ld_\a C^{\a\b}_{ \ \ \ \b}P^{\mu\nu} + C^{\mu\b}_{ \ \ \ \b} J^{\nu\ld}) \right. $$ %%%%%%%%%%%%%%%%%%%%%%%%20%%% \be \left. - C^{\mu\a\b}D^\nu J_{\a\b} + C^{\mu\b}_{ \ \ \ \b} D^\nu J^\a_\a - C^{\ld \b}_{ \ \ \ \b}D^\nu J^\mu _\ld\right], \ee %%%%%%%27 %%%%%%%%%%18%%%%%%%%%25%%%27%%%%25%%522 \be A^{\mu\nu} =Sym \left[ \p^\mu \left(\p^\ld J_\ld{^\nu} - \frac{1}{2} \p^\nu J \right) - \frac{\e^{\mu\nu}}{2} \left(\p^\a \p^\ld J_{\ld\a} - \frac{1}{2} \p^\a \p_\a J \right)\right], \ee %%%19%%%%%%%%%%26%%%%%%%%28%%%%%26%%%523 where $D_{\mu}q=\p_{\mu}q$ and $J= J^\ld_\ld$. The symbol `Sym' in Eqs. (21)-(23) denotes that $\mu$ and $\nu$ should be made symmetric.

620ba102fd7
0 17