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- W4238779726 abstract "We study the zero mode and spontaneous symmetry breaking on the light front (LF). We use the discretized light-cone quantization (DLCQ) of Maskawa and Yamawaki to treat the zero mode in a clean separation from all other modes. It is then shown that the Nambu-Goldstone (NG) phase can be realized on the trivial LF vacuum only when an explicit symmetry-breaking mass of the NG boson ${m}_{ensuremath{pi}}$ is introduced. The NG-boson zero mode integrated over the LF must exhibit a singular behavior $ensuremath{sim}{1/m}_{ensuremath{pi}}^{2}$ in the symmetric limit ${m}_{ensuremath{pi}}ensuremath{rightarrow}0,$ which implies that current conservation is violated at zero mode, or equivalently the LF charge is not conserved even in the symmetric limit. We demonstrate this peculiarity in a concrete model, the linear ensuremath{sigma} model, where the role of the zero-mode constraint is clarified. We further compare our result with the continuum theory. It is shown that in the continuum theory it is difficult to remove the zero mode which is not a single mode with measure zero but the accumulating point causing uncontrollable infrared singularity. A possible way out within the continuum theory is also suggested based on the ``ensuremath{nu} theory.'' We finally discuss another problem of the zero mode in the continuum theory, i.e., the no-go theorem of Nakanishi and Yamawaki on the nonexistence of LF quantum field theory within the framework of Wightman axioms, which remains a challenge for DLCQ, ``ensuremath{nu} theory,'' or any other framework of LF theory." @default.
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- W4238779726 date "1998-04-15" @default.
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- W4238779726 title "Zero mode and symmetry breaking on the light front" @default.
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- W4238779726 doi "https://doi.org/10.1103/physrevd.57.4942" @default.
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