Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation
Apstrakt
We analyze the group-theoretical ramifications of the Nambu-Goldstone (NG) theorem in the self-consistent relativistic variational Gaussian wave functional approximation to spinless field theories. In an illustrative example we show how the Nambu-Goldstone theorem would work in the O(N) symmetric phi(4) scalar field theory, if the residual symmetry of the vacuum were lesser than O(N-1), e.g., if the vacuum were O(N-2), or O(N-3),... symmetric. (This does not imply that any of the lesser vacua is actually the absolute energy minimum: stability analysis has not been done.) The requisite number of NG bosons would be (2N-3), or (3N-6),..., respectively, which may exceed N, the number of elementary fields in the Lagrangian. We show how the requisite new NG bosons would appear even in channels that do not carry the same quantum numbers as one of N elementary particles [scalar field quanta, or Castillejo-Dalitz-Dyson (CDD) poles] in the Lagrangian, i.e., in those flavor channels that have no ...CDD poles. The corresponding Nambu-Goldstone bosons are composites (bound states) of pairs of massive elementary (CDD) scalar fields excitations. As a nontrivial example of this method we apply it to the physically more interesting t Hooft sigma model (an extended N-f=2 bosonic linear sigma model with four scalar and four pseudoscalar fields), with spontaneously and explicitly broken chiral O(4)xO(2)similar or equal toSU(R)(2)xSU(L)(2)xU(A)(1) symmetry. (C) 2003 American Institute of Physics.
Izvor:
Journal of Mathematical Physics, 2003, 44, 7, 2839-2852
DOI: 10.1063/1.1576907
ISSN: 0022-2488
WoS: 000183643000006
Scopus: 2-s2.0-0038675254
Kolekcije
Institucija/grupa
VinčaTY - JOUR AU - Dmitrasinovic, V AU - Nakamura, I PY - 2003 UR - https://vinar.vin.bg.ac.rs/handle/123456789/2640 AB - We analyze the group-theoretical ramifications of the Nambu-Goldstone (NG) theorem in the self-consistent relativistic variational Gaussian wave functional approximation to spinless field theories. In an illustrative example we show how the Nambu-Goldstone theorem would work in the O(N) symmetric phi(4) scalar field theory, if the residual symmetry of the vacuum were lesser than O(N-1), e.g., if the vacuum were O(N-2), or O(N-3),... symmetric. (This does not imply that any of the lesser vacua is actually the absolute energy minimum: stability analysis has not been done.) The requisite number of NG bosons would be (2N-3), or (3N-6),..., respectively, which may exceed N, the number of elementary fields in the Lagrangian. We show how the requisite new NG bosons would appear even in channels that do not carry the same quantum numbers as one of N elementary particles [scalar field quanta, or Castillejo-Dalitz-Dyson (CDD) poles] in the Lagrangian, i.e., in those flavor channels that have no CDD poles. The corresponding Nambu-Goldstone bosons are composites (bound states) of pairs of massive elementary (CDD) scalar fields excitations. As a nontrivial example of this method we apply it to the physically more interesting t Hooft sigma model (an extended N-f=2 bosonic linear sigma model with four scalar and four pseudoscalar fields), with spontaneously and explicitly broken chiral O(4)xO(2)similar or equal toSU(R)(2)xSU(L)(2)xU(A)(1) symmetry. (C) 2003 American Institute of Physics. T2 - Journal of Mathematical Physics T1 - Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation VL - 44 IS - 7 SP - 2839 EP - 2852 DO - 10.1063/1.1576907 ER -
@article{ author = "Dmitrasinovic, V and Nakamura, I", year = "2003", abstract = "We analyze the group-theoretical ramifications of the Nambu-Goldstone (NG) theorem in the self-consistent relativistic variational Gaussian wave functional approximation to spinless field theories. In an illustrative example we show how the Nambu-Goldstone theorem would work in the O(N) symmetric phi(4) scalar field theory, if the residual symmetry of the vacuum were lesser than O(N-1), e.g., if the vacuum were O(N-2), or O(N-3),... symmetric. (This does not imply that any of the lesser vacua is actually the absolute energy minimum: stability analysis has not been done.) The requisite number of NG bosons would be (2N-3), or (3N-6),..., respectively, which may exceed N, the number of elementary fields in the Lagrangian. We show how the requisite new NG bosons would appear even in channels that do not carry the same quantum numbers as one of N elementary particles [scalar field quanta, or Castillejo-Dalitz-Dyson (CDD) poles] in the Lagrangian, i.e., in those flavor channels that have no CDD poles. The corresponding Nambu-Goldstone bosons are composites (bound states) of pairs of massive elementary (CDD) scalar fields excitations. As a nontrivial example of this method we apply it to the physically more interesting t Hooft sigma model (an extended N-f=2 bosonic linear sigma model with four scalar and four pseudoscalar fields), with spontaneously and explicitly broken chiral O(4)xO(2)similar or equal toSU(R)(2)xSU(L)(2)xU(A)(1) symmetry. (C) 2003 American Institute of Physics.", journal = "Journal of Mathematical Physics", title = "Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation", volume = "44", number = "7", pages = "2839-2852", doi = "10.1063/1.1576907" }
Dmitrasinovic, V.,& Nakamura, I.. (2003). Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation. in Journal of Mathematical Physics, 44(7), 2839-2852. https://doi.org/10.1063/1.1576907
Dmitrasinovic V, Nakamura I. Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation. in Journal of Mathematical Physics. 2003;44(7):2839-2852. doi:10.1063/1.1576907 .
Dmitrasinovic, V, Nakamura, I, "Dynamical symmetry breaking and the Nambu-Goldstone theorem in the Gaussian wave functional approximation" in Journal of Mathematical Physics, 44, no. 7 (2003):2839-2852, https://doi.org/10.1063/1.1576907 . .