Wave packet dynamics in Yang-Mills theory

We analyze the Hamiltonian time evolution of classical SU(2) Yang-Mills-Higgs theory with a fundamental Higgs doublet on a spacial lattice. In particular, we study energy transfer and equilibration processes among the gauge and Higgs sectors, calculate the maximal Lyapunov exponents under randomized initial conditions in the weak-coupling regime, where one expects them to be related to the high-temperature plasmon damping rate, and investigate their energy and coupling dependence. We further examine finite-time and finite-size errors, study the impact of the Higgs fields on the instability of constant non-Abelian magnetic fields, and comment on the implications of our results for the thermalization properties of hot gauge fields in the presence of matter.

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“…(Related findings for the scattering of two classical SU(2) YM and YMH wave packets [95] were reported in Ref. [80]. )…”

Section: B Nuclear Collisionssupporting

confidence: 66%

Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice

Fariello

Forkel

2009

Phys. Rev. D

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“…Ref. [10] studies the YangMills-Higgs system in a 2-dimensional plane-wave Ansatz and again finds that momentum can be efficiently redistributed. It is the purpose of our investigation to shed further light on the situation in 4-dimensions in the presence of a Higgs field and to investigate the relation between incoming particle number and topology change.…”

Section: Introductionmentioning

confidence: 99%

Computational study of baryon number violation in high energy electroweak collisions

Rebbi

Singleton

1996

Phys. Rev. D

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We use semiclassical methods to study processes which give rise to change of topology and therefore to baryon number violation in the standard model. We consider classically allowed processes, i.e. energies above the sphaleron barrier. We develop a computational procedure that allows us to solve the Yang Mills equations of motion for spherically symmetric configurations and to identify the particle numbers of the in-and out-states. A stochastic sampling technique is then used to map the region spanned by the topology changing solutions in the energy versus incoming particle number plane and, in particular, to determine its lower boundary. A lower boundary which approaches small particle number would be a strong indication that baryon number violation would occur in high energy collisions, whereas a lower asymptote at large particle number would be evidence of the contrary. With our method and the computational resources we have had at our disposal, we have been able to determine the lower boundary up to energies approximately equal to one and a half time times the sphaleron energy and observed a 40% decrease in particle number with no sign of the particle number leveling off. However encouraging this may be, the decrease in incoming particle number is only from 50 particles down to approximately 30. Nevertheless, the formalism we have established will make it possible to extend the scope of this investigation and also to study processes in the classically forbidden region, which we plan to do in the future. BUHEP-95-33Submitted to Physical Review D hep-ph/9601260Typeset in REVT E X

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“…From the analytic viewpoint, the situation could appear to be hopeless. In (3+1)-dimensional Yang-Mills theory, already the collision of (topologically trivial) plane waves is intractable and numerical methods must be used 1 (see [34][35][36][37][38][39][40] and references therein). Thus, one might think that the analysis of processes (such as collisions) of solitonic-like configurations with non-vanishing topological charge should be "even more intractable" with analytic methods.…”

Section: Introductionmentioning

confidence: 99%

Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

Canfora

2021

Eur. Phys. J. C

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An infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

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Wave packet dynamics in Yang-Mills theory

Cited by 14 publications

References 12 publications

Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice

Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice

Computational study of baryon number violation in high energy electroweak collisions

Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

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