We extend the Gutzwiller trace formula to systems of noninteracting identicalparticles. The standard relation for isolated orbits does not apply since theenergy of each particle is separately conserved causing the periodic orbits tooccur in continuous families. The identical nature of the particles alsointroduces discrete permutational symmetries. We exploit the formalism ofCreagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studiedsemiclassical dynamics in the presence of continuous symmetries, to derivemany-body trace formulas for the full and symmetry-reduced densities of states.Numerical studies of the three-particle cardioid billiard are used toexplicitly illustrate and test the results of the theory.
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机译：我们将Gutzwiller跟踪公式扩展到非相互作用的相同粒子的系统。孤立轨道的标准关系不适用，因为每个粒子的能量被分别保存，导致周期性轨道以连续的族出现。粒子的相同性质还引入了离散的排列对称性。我们利用了Creagh和Littlejohn [Phys。 Rev. A 44，836（1991）]，他们研究了连续对称性存在下的半经典动力学，得出了全体和对称性降低的状态密度的多体跟踪公式。对三粒子心型台球进行了数值研究明确说明和检验该理论的结果。
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