Dirac Variables in Gauge Theories

The review is devoted to a relativistic formulation of therst Dirac quantization of QED (1927) and its generalization to the non-Abelian theories (YangAMills and QCD) with the topological degeneration of initial data. Using the Dirac variables we give a systematic description of relativistic nonlocal bound states in QED with a choice of the time axis of quantization along the eigenvectors of their total momentum operator. We show that the Dirac variables of the non-Abelianelds are topologically degenerated, and there is a pure gauge Higgs effect in the sector of the zero winding number that leads to a nonperturbative physical vacuum in the form of the WuAYang monopole. Phases of the topological degeneration in the new perturbation theory are determined by an equation of the Gribov ambiguity of the constraint-shell gauge dened as an integral of the Gauss equation with zero initial data. The constraint-shell non-Abelian dynamics includes zero mode of the Gauss-law differential operator, and a rising potential of the instantaneous interaction, that rearranges the perturbation series and changes the asymptotic freedom formula. The Dirac variables with the topological degeneration of initial data describe color connement in the form of quark- hadron duality as a consequence of summing over the Gribov copies. A solution of U (1) problem is given by mixing the zero mode with η0 meson. We discuss reasons why all these physical effects disappear for arbitrary gauges of physical sources in the standard FaddeevAPopov integral. �i§µ· ¶µ¸¢OÐ¥´ ·¥²OE¨¢¨¸E¸±µ° Eµ·³E²¨·µ¢±¥ ¶¥·¢µ£µ ¤¨· ±µ¢¸±µ£µ ±¢ ´Eµ¢ ´¨O ¨ ¥£µ µiµiÐ¥´¨O ´ ´¥ i¥²¥¢O E¥µ·¨¨ Ÿ´£aAŒ¨²²¸ ¨ S•" ¸ Eµ¶µ²µ£¨I¥¸±¨³ ¢O·µ|¤¥´¨¥³ ´ I ²O- ´OI ¤ ´´OI. ŒO ¨¸¶µ²O§E¥³ ·¥²OE¨¢¨¸E¸±¨-±µ¢ ·¨ ´E´µ¥ µ¶·¥¤¥²¥´¨¥ ¤¨· ±µ¢¸±¨I ± ²¨i·µ¢µI- ´µ-¨´¢ ·¨ ´E´OI ¶¥·¥³¥´´OI, § ¤ ´´OI ´ ¶µ¢¥·I´µ¸E¨ ¸¢O§¥° (�µ²Ei ·¨´µ¢, 1965), ¤²O ¸¨¸E¥- ³ E¨I¥¸±µ£µ µ¶¨¸ ´¨O ´¥²µ± ²O´OI ¸¢O§ ´´OI ¸µ¸EµO´¨° ¢ S�", ¢Oi¨· O µ¸O ¢·¥³¥´¨ ¢¤µ²O ¸µi¸E¢¥´´OI ¢¥±Eµ·µ¢ µ¶¥· Eµ· ¶µ²´µ£µ ¨³¶E²O¸ E¨§¨I¥¸±¨I ¸µ¸EµO´¨°, IEµiO E¤µ¢²¥E¢µ·¨EO E¸²µ¢¨O Œ ·±µ¢ A�± ¢O (E. ¥. E¸²µ¢¨O ´¥¶·¨¢µ¤¨³µ¸E¨ ´¥²µ± ²O´OI ¶·¥¤¸E ¢²¥´¨° £·E¶¶O �E ´± ·¥). �µ± § ´µ, IEµ ¶·O³µ¥ µiµiÐ¥´¨¥ ¤¨· ±µ¢¸±¨I ¶¥·¥³¥´´OI ´ ´¥ i¥²¥¢E E¥µ·¨O ¢¥¤¥E ± ¨I Eµ¶µ²µ£¨I¥¸±µ³E ¢O·µ|¤¥´¨O ¢ Eµ·³¥ £·¨iµ¢¸±¨I ±µ¶¨° ± ²¨i·µ¢±¨, ±µEµ· O O¢²O- ¥E¸O ¨´E¥£· ²µ³ E· ¢´¥´¨O ƒ E¸¸ ¸ ´E²¥¢O³¨ ´ I ²O´O³¨ ¤ ´´O³¨. "· ¢´¥´¨¥ ƒ·¨iµ¢ µ¤´µ- §´ I´µ µ¶·¥¤¥²O¥E E §O Eµ¶µ²µ£¨I¥¸±¨I ¶·¥µi· §µ¢ ´¨° ¨ ¨I ®´µ¸¨E¥²O¯ ¢ ¢¨¤¥ ¨E· ±· ¸´µ- ·¥£E²O·¨§µ¢ ´´µ£µ ³µ´µ¶µ²O ‚EAŸ´£ . "¨´ ³¨± ´¥ i¥²¥¢OI E¥µ·¨° ´ ¶µ¢¥·I´µ¸E¨ ¸¢O§¥° ¢±²OI ¥E ´E²¥¢EO ³µ¤E E· ¢´¥´¨O ¸¢O§¨ ¨ · ¸EEШ° ¶µE¥´I¨ ² µ¤´µ¢·¥³¥´´µ£µ ¢§ ¨³µ¤¥°¸E¢¨O Eµ±µ¢. �·µi²¥³ £·¨iµ¢¸±¨I ´E²¥° ¤¥E¥·³¨´ ´E " ¤¤¥¥¢ A�µ¶µ¢ ·¥I ¥E¸O ¶EE¥³ ¶µ¸E·µ¥´¨O ¤¥±¢ E´µ£µ ¨´E¥£· ² "¥°´³ ´ , ¸µ¤¥·| Ð¥£µ ¨´E¥£·¨·µ¢ ´¨¥ ¶µ ´E²¥¢O³ ³µ¤ ³. �¥²OE¨¢¨¸E- ¸± O Eµ·³E²¨·µ¢± S•" ´ ¶µ¢¥·I´µ¸E¨ ¸¢O§¥° ¸ Eµ¶µ²µ£¨I¥¸±¨³ ¢O·µ|¤¥´¨¥³ ´ I ²O´OI ¤ ´- ´OI µ¶¨¸O¢ ¥E ±µ´¸E¨EEe´E´O¥ ³ ¸¸O ±¢ ·±µ¢ ¨ £²Oµ´µ¢, ³µ¤¨E¨± I¨O Eµ·³E²O ¸¨³¶EµE¨I¥- ¸±µ° ¸¢µiµ¤O, ¸¶µ´E ´´µ¥ ´ ·EI¥´¨¥ ±¨· ²O´µ° ¸¨³³¥E·¨¨, ±µ´E °´³¥´E I¢¥E´OI ¸µ¸EµO´¨° ¢ Eµ·³¥ ±¢ ·±- ¤·µ´´µ° ¤E ²O´µ¸E¨ (± ± ¸²¥¤¸E¢¨¥ E¸·¥¤´¥´¨O ¶µ Eµ¶µ²µ£¨I¥¸±µ³E ¢O·µ|¤¥´¨O) ¨ ¤µ¶µ²´¨E¥²O´EO ³ ¸¸E ¤¥¢OEµ£µ ¶¸¥¢¤µ¸± ²O·´µ£µ ³¥§µ´ (± ± ¸²¥¤¸E¢¨¥ ¸³¥I¨¢ ´¨O OEµ£µ ³¥- §µ´ ¸ ´E²¥¢µ° ³µ¤µ°). ŒO µi¸E|¤ ¥³ ¶·¨I¨´O ¨¸I¥§´µ¢¥´¨O ¢¸¥I OE¨I OEE¥±Eµ¢ ¶·¨ ¶¥·¥Iµ¤¥ ± ¨´E¥£· ²E " ¤¤¥¥¢ A�µ¶µ¢ ¸ ¶·µ¨§¢µ²O´µ° ± ²¨i·µ¢±µ°.