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.
040
Stable Diffusion
raw photo captured with Fujifilm GFX 100 II, Velvia/Vivid mode, low key lighting, high contrast, ISO 100, with GF 110mm f/2 R LM WR lens. Cinematic hyper-realistic candid action shot of a young, strikingly beautiful Central Asian Turkic female shaman captured mid-dance within the oppressive ruins of an ancient stone temple on a vast, windswept dark steppe. She is caught in a dynamic, unposed moment, gracefully turning while striking a large, ancient hide-stretched frame drum, intricately carved bone mallets held elegantly in her clean, unblemished hands. Her expression is naturally captivating and commanding—eyes half-lidded with smoldering intensity gazing downward into the rhythmic motion rather than at the camera, full lips slightly parted in focused breath, a subtle knowing half-smile radiating raw spiritual strength fused with potent feminine allure. Her skin is luminous and beautifully smooth with realistic, healthy pores and a subtle natural sweat sheen, free from harsh weathering, scars, or aging marks. Micro-textures highlight the rich, cracked organic surface of the aged hide drum and authentically worn bone mallets. Lighting follows dual-source chiaroscuro: low exposure, extreme high contrast with intense warm orange glow from crackling braziers carving her graceful silhouette and drum, while deep cold crushing shadows from the stone ruins swallow the background. Dense volumetric ritual smoke and steppe dust create atmospheric Mie scattering, with swirling particles dancing around her moving figure. Rich desaturated dark tones, burning orange accents, ice-cold stone grays. Captured candidly on Leica SL2, GF 110mm f/2 R LM WR lens, wide open aperture, low key, high contrast, ISO 64, Classic Negative simulation. Photorealistic gothic atmosphere, kinetic elegance, hyper-detailed masterpiece, 1:1 composition.
07
Z Image
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.
040
Stable Diffusion
raw photo captured with Fujifilm GFX 100 II, Velvia/Vivid mode, low key lighting, high contrast, ISO 100, with GF 110mm f/2 R LM WR lens. Cinematic hyper-realistic candid action shot of a young, strikingly beautiful Central Asian Turkic female shaman captured mid-dance within the oppressive ruins of an ancient stone temple on a vast, windswept dark steppe. She is caught in a dynamic, unposed moment, gracefully turning while striking a large, ancient hide-stretched frame drum, intricately carved bone mallets held elegantly in her clean, unblemished hands. Her expression is naturally captivating and commanding—eyes half-lidded with smoldering intensity gazing downward into the rhythmic motion rather than at the camera, full lips slightly parted in focused breath, a subtle knowing half-smile radiating raw spiritual strength fused with potent feminine allure. Her skin is luminous and beautifully smooth with realistic, healthy pores and a subtle natural sweat sheen, free from harsh weathering, scars, or aging marks. Micro-textures highlight the rich, cracked organic surface of the aged hide drum and authentically worn bone mallets. Lighting follows dual-source chiaroscuro: low exposure, extreme high contrast with intense warm orange glow from crackling braziers carving her graceful silhouette and drum, while deep cold crushing shadows from the stone ruins swallow the background. Dense volumetric ritual smoke and steppe dust create atmospheric Mie scattering, with swirling particles dancing around her moving figure. Rich desaturated dark tones, burning orange accents, ice-cold stone grays. Captured candidly on Leica SL2, GF 110mm f/2 R LM WR lens, wide open aperture, low key, high contrast, ISO 64, Classic Negative simulation. Photorealistic gothic atmosphere, kinetic elegance, hyper-detailed masterpiece, 1:1 composition.
07
Z Image
raw photo captured with Fujifilm GFX 100 II, Velvia/Vivid mode, low key lighting, high contrast, ISO 100, with GF 110mm f/2 R LM WR lens. Cinematic hyper-realistic candid action shot of a young, strikingly beautiful Central Asian Turkic female shaman captured mid-dance within the oppressive ruins of an ancient stone temple on a vast, windswept dark steppe. She is caught in a dynamic, unposed moment, gracefully turning while striking a large, ancient hide-stretched frame drum, intricately carved bone mallets held elegantly in her clean, unblemished hands. Her expression is naturally captivating and commanding—eyes half-lidded with smoldering intensity gazing downward into the rhythmic motion rather than at the camera, full lips slightly parted in focused breath, a subtle knowing half-smile radiating raw spiritual strength fused with potent feminine allure. Her skin is luminous and beautifully smooth with realistic, healthy pores and a subtle natural sweat sheen, free from harsh weathering, scars, or aging marks. Micro-textures highlight the rich, cracked organic surface of the aged hide drum and authentically worn bone mallets. Lighting follows dual-source chiaroscuro: low exposure, extreme high contrast with intense warm orange glow from crackling braziers carving her graceful silhouette and drum, while deep cold crushing shadows from the stone ruins swallow the background. Dense volumetric ritual smoke and steppe dust create atmospheric Mie scattering, with swirling particles dancing around her moving figure. Rich desaturated dark tones, burning orange accents, ice-cold stone grays. Captured candidly on Leica SL2, GF 110mm f/2 R LM WR lens, wide open aperture, low key, high contrast, ISO 64, Classic Negative simulation. Photorealistic gothic atmosphere, kinetic elegance, hyper-detailed masterpiece, 1:1 composition.
07
Z Image
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.
040
Stable Diffusion
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.
040
Stable Diffusion
raw photo captured with Fujifilm GFX 100 II, Velvia/Vivid mode, low key lighting, high contrast, ISO 100, with GF 110mm f/2 R LM WR lens. Cinematic hyper-realistic candid action shot of a young, strikingly beautiful Central Asian Turkic female shaman captured mid-dance within the oppressive ruins of an ancient stone temple on a vast, windswept dark steppe. She is caught in a dynamic, unposed moment, gracefully turning while striking a large, ancient hide-stretched frame drum, intricately carved bone mallets held elegantly in her clean, unblemished hands. Her expression is naturally captivating and commanding—eyes half-lidded with smoldering intensity gazing downward into the rhythmic motion rather than at the camera, full lips slightly parted in focused breath, a subtle knowing half-smile radiating raw spiritual strength fused with potent feminine allure. Her skin is luminous and beautifully smooth with realistic, healthy pores and a subtle natural sweat sheen, free from harsh weathering, scars, or aging marks. Micro-textures highlight the rich, cracked organic surface of the aged hide drum and authentically worn bone mallets. Lighting follows dual-source chiaroscuro: low exposure, extreme high contrast with intense warm orange glow from crackling braziers carving her graceful silhouette and drum, while deep cold crushing shadows from the stone ruins swallow the background. Dense volumetric ritual smoke and steppe dust create atmospheric Mie scattering, with swirling particles dancing around her moving figure. Rich desaturated dark tones, burning orange accents, ice-cold stone grays. Captured candidly on Leica SL2, GF 110mm f/2 R LM WR lens, wide open aperture, low key, high contrast, ISO 64, Classic Negative simulation. Photorealistic gothic atmosphere, kinetic elegance, hyper-detailed masterpiece, 1:1 composition.
07
Z Image
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.
040
Stable Diffusion
raw photo captured with Fujifilm GFX 100 II, Velvia/Vivid mode, low key lighting, high contrast, ISO 100, with GF 110mm f/2 R LM WR lens. Cinematic hyper-realistic candid action shot of a young, strikingly beautiful Central Asian Turkic female shaman captured mid-dance within the oppressive ruins of an ancient stone temple on a vast, windswept dark steppe. She is caught in a dynamic, unposed moment, gracefully turning while striking a large, ancient hide-stretched frame drum, intricately carved bone mallets held elegantly in her clean, unblemished hands. Her expression is naturally captivating and commanding—eyes half-lidded with smoldering intensity gazing downward into the rhythmic motion rather than at the camera, full lips slightly parted in focused breath, a subtle knowing half-smile radiating raw spiritual strength fused with potent feminine allure. Her skin is luminous and beautifully smooth with realistic, healthy pores and a subtle natural sweat sheen, free from harsh weathering, scars, or aging marks. Micro-textures highlight the rich, cracked organic surface of the aged hide drum and authentically worn bone mallets. Lighting follows dual-source chiaroscuro: low exposure, extreme high contrast with intense warm orange glow from crackling braziers carving her graceful silhouette and drum, while deep cold crushing shadows from the stone ruins swallow the background. Dense volumetric ritual smoke and steppe dust create atmospheric Mie scattering, with swirling particles dancing around her moving figure. Rich desaturated dark tones, burning orange accents, ice-cold stone grays. Captured candidly on Leica SL2, GF 110mm f/2 R LM WR lens, wide open aperture, low key, high contrast, ISO 64, Classic Negative simulation. Photorealistic gothic atmosphere, kinetic elegance, hyper-detailed masterpiece, 1:1 composition.
07
Z Image
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.
040
Stable Diffusion
raw photo captured with Fujifilm GFX 100 II, Velvia/Vivid mode, low key lighting, high contrast, ISO 100, with GF 110mm f/2 R LM WR lens. Cinematic hyper-realistic candid action shot of a young, strikingly beautiful Central Asian Turkic female shaman captured mid-dance within the oppressive ruins of an ancient stone temple on a vast, windswept dark steppe. She is caught in a dynamic, unposed moment, gracefully turning while striking a large, ancient hide-stretched frame drum, intricately carved bone mallets held elegantly in her clean, unblemished hands. Her expression is naturally captivating and commanding—eyes half-lidded with smoldering intensity gazing downward into the rhythmic motion rather than at the camera, full lips slightly parted in focused breath, a subtle knowing half-smile radiating raw spiritual strength fused with potent feminine allure. Her skin is luminous and beautifully smooth with realistic, healthy pores and a subtle natural sweat sheen, free from harsh weathering, scars, or aging marks. Micro-textures highlight the rich, cracked organic surface of the aged hide drum and authentically worn bone mallets. Lighting follows dual-source chiaroscuro: low exposure, extreme high contrast with intense warm orange glow from crackling braziers carving her graceful silhouette and drum, while deep cold crushing shadows from the stone ruins swallow the background. Dense volumetric ritual smoke and steppe dust create atmospheric Mie scattering, with swirling particles dancing around her moving figure. Rich desaturated dark tones, burning orange accents, ice-cold stone grays. Captured candidly on Leica SL2, GF 110mm f/2 R LM WR lens, wide open aperture, low key, high contrast, ISO 64, Classic Negative simulation. Photorealistic gothic atmosphere, kinetic elegance, hyper-detailed masterpiece, 1:1 composition.
07
Z Image