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arXiv 0711.0075hep-th
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量子场论中对称破缺后的玻色子

Bosons after Symmetry Breaking in Quantum Field Theory

Takehisa Fujita, Makoto Hiramoto, Hidenori Takahashi

摘要:

本文给出了费米子场论中自发对称性破缺及其玻色子的统一描述。在Nambu-Jona-Lasinio、Thirring和QCD $_2$的费米子场论模型中,当手征对称性在新真空中自发破缺后,不存在Goldstone玻色子。阐明了Goldstone定理的缺陷,指出Goldstone定理预言的“无质量玻色子”是虚的,只对应于一个$free$无质量费米子和反费米子对。进一步讨论了Thirring模型的Bethe对称解的精确谱,得到了所有物理量的解析表达式,使我们能够更深入地理解自发对称性破缺的本质.此外,我们还研究了量子色动力学$_2$中的玻色子谱,并证明了对于$SU(N_c)$色,玻色子总是具有有限的质量。讨论了QCD $_2$中的光锥处方问题,指出平凡光锥真空是导致玻色子质量预测错误的原因。

英文摘要:

We present a unified description of the spontaneous symmetry breaking and its associated bosons in fermion field theory. There is no Goldstone boson in the fermion field theory models of Nambu-Jona-Lasinio, Thirring and QCD$_2$ after the chiral symmetry is spontaneously broken in the new vacuum. The defect of the Goldstone theorem is clarified, and the "massless boson" predicted by the theorem is virtual and corresponds to just a $free$ massless fermion and antifermion pair. Further, we discuss the exact spectrum of the Thirring model by the Bethe ansatz solutions, and the analytical expressions of all the physical observables enable us to understand the essence of the spontaneous symmetry breaking in depth. Also, we examine the boson spectrum in QCD$_2$, and show that bosons always have a finite mass for $SU(N_c)$ colors. The problem of the light cone prescription in QCD$_2$ is discussed, and it is shown that the trivial light cone vacuum is responsible for the wrong prediction of the boson mass.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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