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Volume 23, Issue 2
Theory of Spontaneous Symmetry Breaking and an Application to Superconductivity: Nambu-Goldstone and Higgs Excitation Modes

Takashi Yanagisawa

DOI: 10.4208/cicp.OA-2017-0057

Commun. Comput. Phys., 23 (2018), pp. 459-475.

Published online: 2018-02

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  • Abstract

We present a general framework of the theory of spontaneous symmetry breaking in non-relativistic systems. We discuss a spontaneous symmetry breaking in a system with general global symmetry given by a Lie group G. The Nambu-Goldstone boson and Higgs boson are represented explicitly by local fields by means of the basis of the Lie algebra of G. An application to superconductivity is discussed. We evaluate the Green's functions of the Nambu-Goldstone and Higgs bosons in superconductors. We show that the Nambu-Goldstone and Higgs modes exhibit interesting behaviors in multi-component superconductors.

  • Keywords

Spontaneous symmetry breaking, Lie algebra, Nambu-Goldstone boson, Higgs boson, Ward-Takahashi identity, superconductivity, multi-band superconductor.

  • AMS Subject Headings

22E, 22C, 70H, 70S

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-23-459, author = {Takashi Yanagisawa}, title = {Theory of Spontaneous Symmetry Breaking and an Application to Superconductivity: Nambu-Goldstone and Higgs Excitation Modes}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {2}, pages = {459--475}, abstract = {

We present a general framework of the theory of spontaneous symmetry breaking in non-relativistic systems. We discuss a spontaneous symmetry breaking in a system with general global symmetry given by a Lie group G. The Nambu-Goldstone boson and Higgs boson are represented explicitly by local fields by means of the basis of the Lie algebra of G. An application to superconductivity is discussed. We evaluate the Green's functions of the Nambu-Goldstone and Higgs bosons in superconductors. We show that the Nambu-Goldstone and Higgs modes exhibit interesting behaviors in multi-component superconductors.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0057}, url = {http://global-sci.org/intro/article_detail/cicp/10533.html} }
TY - JOUR T1 - Theory of Spontaneous Symmetry Breaking and an Application to Superconductivity: Nambu-Goldstone and Higgs Excitation Modes AU - Takashi Yanagisawa JO - Communications in Computational Physics VL - 2 SP - 459 EP - 475 PY - 2018 DA - 2018/02 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2017-0057 UR - https://global-sci.org/intro/article_detail/cicp/10533.html KW - Spontaneous symmetry breaking, Lie algebra, Nambu-Goldstone boson, Higgs boson, Ward-Takahashi identity, superconductivity, multi-band superconductor. AB -

We present a general framework of the theory of spontaneous symmetry breaking in non-relativistic systems. We discuss a spontaneous symmetry breaking in a system with general global symmetry given by a Lie group G. The Nambu-Goldstone boson and Higgs boson are represented explicitly by local fields by means of the basis of the Lie algebra of G. An application to superconductivity is discussed. We evaluate the Green's functions of the Nambu-Goldstone and Higgs bosons in superconductors. We show that the Nambu-Goldstone and Higgs modes exhibit interesting behaviors in multi-component superconductors.

Takashi Yanagisawa. (2018). Theory of Spontaneous Symmetry Breaking and an Application to Superconductivity: Nambu-Goldstone and Higgs Excitation Modes. Communications in Computational Physics. 23 (2). 459-475. doi:10.4208/cicp.OA-2017-0057
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