We construct an extension of the standard Kogut-Susskind lattice model for classical 3+1 dimensional Yang-Mills theory, in which "classical particle" degrees of freedom are added. We argue that this will correctly reproduce the "hard thermal loop" effects of hard degrees of freedom, while giving a local implementation which is numerically tractable. We prove that the extended system is Hamiltonian and has the same thermodynamics as dimensionally reduced hot Yang-Mills theory put on a lattice. We present a numerical update algorithm and study the abelian theory to verify that the classical gauge theory self-energy is correctly modified. Then we use the extended system to study the diffusion constant for Chern-Simons number. We verify the Arnold-Son-Yaffe picture that the diffusion constant is inversely proportional to hard thermal loop strength. Our numbers correspond to a diffusion constant of Γ = 29 ± 6α

We propose a formulation of the long-distance dynamics of gauge theories at finite temperature on a lattice in Minkowski space, including the effects of hard thermal loops on the dynamics of the long wavelength modes. Our approach is based on the dual classical limits of quantum fields as waves and particles in the infrared and ultraviolet limits, respectively. It exhibits manifest invariance under space-dependent lattice gauge transformations and conserves Gauss' law. 02.60.Cb, 11.15.Ha, 11.15.Kc, 12.38.Mh

We investigate thermalization processes occurring at different time scales in the Yang-Mills-Higgs system at high temperatures. We determine the largest Lyapunov exponent associated with the gauge fields and verify its relation to the perturbatively calculated damping rate of a static gauge boson. ͓S0556-2821͑97͒03304-3͔

We discuss the results of numerical simulations of colliding wavepackets in SU(2) Yang-Mills theory. We investigate their behavior as a function of amplitude and momentum distribution. We find regions in our parameter space in which initial wave packets scatter into final configurations with dramatically different momentum distributions. These results constitute new classical trajectories with multiparticle boundary conditions. We explain their relevance for the calculation of scattering amplitudes in the semiclassical approximation. Finally, we give directions for future work.

I. IN T R O D U C T IO NT he i dea ofthe restorati on ofspontaneousl y broken gauge sym m etri esunderextrem e condi ti ons(hi gh tem perature, hi gh ferm i on densi ti es, strong external gauge el ds) was i ntensel y studi ed i n the 1970' s and i s wel l know n [ 1, 2] (for revi ew see [ 3,4] ). U nder these condi ti ons spontaneousl y broken gauge theori es undergo vari ous phase transi ti ons resul ti ng,i n m ostcases,i n the restorati on ofthe ori gi nal l y broken sym m etri es.T heconsequencesofsuch restorati on| m assl essnessofthe gauge bosons and ferm i ons,l ong range characterofthe i nteracti ons,etc. | are very i m portant for the properti es ofthe very earl y U ni verse. T hese properti es m ay al so pl ay a si gni cant rol e i n the context ofneutron stars and i n the m ul ti parti cl e producti on at hi gh-energy i nteracti ons.It has l ong been real i zed [ 1,2]that the Lagrangi an of the Standard M odelw i th a non-zero vacuum expectati on val ue forthe scal ar el d i sa covari antgeneral i zati on ofthe G i nzburg-Landau equati on w hi ch descri besa w i de vari ety of\ordered" system s (ferrom agnets,super ui ds,superconductors,crystal s,etc. ) and thei r phase transi ti ons. From thi s poi nt of vi ew very di erent system s have com m on generalproperti es due to thei r di erentl y reveal ed broken sym m etri es. U si ng the anal ogy w i th superconducti vi ty,w here a strong externalel ectrom agneti c current (m agneti c el d)destroyssuperconducti vi ty resul ti ng i n thetransi ti on to thenorm alstate,an i ntensecurrentofweakl y i nteracti ng parti cl es (e. g. ofW -bosons) can restore the gauge sym m etry and cause the transi ti on to a new phase w i th m assl ess gauge quanta [ 2,5] .T he present paper i s devoted to the study ofthe restorati on ofthe spontaneousl y broken gauge sym m etry i n the col l i si ons of i ntense, energeti c W -boson wave packets. T he paper i s organi zed as fol l ow s. Secti on II descri bes the sym m etry restorati on atzero tem peraturei n the SU (2)H i ggsm odel .In Secti on IIIthi sphenom enon i scom pared w i th the wel l -know n resul ts ofsym m etry restorati on at hi gh tem perature. Secti on IV i s devoted to the stabi l i ty probl em ofthe one-l oop radi ati vel y corrected e ecti ve potenti alw i th the externalgauge el d i n the l i ght ofthe exi stence of the heavy t-quark. In Secti on V we present l atti ce cal cul ati ons ofgauge boson wave packet col l i si ons i n w hi ch the restorati on ofthe SU (2) gauge sym m etry i s m ani fested. Secti on V Icontai ns short concl udi ng rem arks. II. R E ST O R A T IO N O F T H E B R O K E N SU (2) SY M M E T R Y B Y A N IN T E N SE G A U G E F IE L DT hi s paper i s an outgrow th ofprevi ous studi es ofthe i nteracti ons ofgauge el d wave packets i n the SU (2) Yang-M i l l s [ 6]and Yang-M i l l s-H i ggs [ 7]theori es. B ei ng i n essense cl assi cal ,the approach ofthese publ i cati ons nonethel ess reveali nteresti ng phenom ena associ ated w i th the non-perturbati vedescri pti on ofm ul ti par...