22 pages, 6 figures, v2: typos fixed, appendix B extended, improved pictures format, v3: prepared for submission to Nuclear Physics B, typos fixed, added some two-loop two-point functions, v4: published version
We present the way to continue the bosonic Thirring model or $βγ$-system with quartic interaction to Minkowski signature, based on the symmetries of this model. It is shown that the considered Minkowski version of the model is one-loop renormalizable. Based on this, we find the amplitudes of the scattering of the excitations corresponding to the $γ$ and $\barγ$ fields up to the one-loop order. In particular, it was computed that the $2 \rightarrow 2$ amplitudes of these excitations possess the property of reflectionless scattering and thus the corresponding $S$-matrix of such excitations satisfies the Yang-Baxter equation. The obtained $S$-matrix elements for $γ$ and $\barγ$ are shown to coincide with the corresponding $S$-matrix elements of the solitons in the complex sine-Gordon model proposed by Dorey and Hollowood.
Bosonic vacuum wave functions from the BCS-type wave function of the ground state of the massless Thirring model
BCS型波函数描述了无质量Thirring模型的基态，它是手性破缺相.费米子场在旋断相玻色子中量子化的无质量Thirring模型，统一为自由无质量（伪）标量场的量子场论（Eur. C20，723（2001））。本文从BCS型波函数出发，通过对Thirring费米子场的量子涨落进行平均，得到了自由无质量（赝）标量场基态的波函数。我们证明了这些波函数是正交的，归一化的，在无质量（伪）标量场的位移下是非不变的。这证明了自由无质量（伪）标量场的量子场论中场移对称性的自发破缺。我们证明了对玻色化BCS型波函数计算的真空-真空跃迁振幅与仅由振动模贡献定义的格林函数的生成泛函一致（Eur. J. C 24，653（2002））。这证实了玻色化BCS型波函数由集体零模（hep-th/0212226）定义的假设。我们认为所得结果不是Mermin-Wagner-Hohenberg定理和Coleman定理的反例。
The Nambu-Goto Theory of Closed Bosonic Strings Moving in 1+3-Dimensional Minkowski Space: The Construction of the Quantum Algebra of Observables up to Degree Five
Quantum Bosonic String Energy-Momentum Tensor in Minkowski Space-Time
计算了闵可夫斯基时空中弦的量子能量动量张量${\hat T}^{μν}(x)$。我们计算了它的期望值为不同的物理弦状态的开放和封闭的玻色弦。所考虑的状态描述的规范化波包的质心坐标。我们特别发现，${\hat T}^{μν}(x)$是{ \bf有限}的，这可能意味着，当我们接近弦位置时，在弦论中发生的经典发散在量子水平上被消除了，因为弦的位置被量子涨落弄模糊了。对于大质量弦态，${\hat T}^{μν}(x)$的期望值在首阶为零（亏格为零）。对于无质量弦态，它有一个非零值，我们明确计算和分析球对称和圆柱对称波包。能量-动量张量分量作为一个无质量的块向外传播，峰值在$ r = t $。
