Linear Sigma model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action
Апстракт
We show an explicit connection between the solution to the equations of motion in the Gaussian functional approximation [I. Nakamura, V. Dmitrasinovic, Prog. Theor. Phys. 106 (2001) 11951 and the minimum of the (Gaussian) effective potential/action of the linear Sigma model, as well as with the N/D method in dispersion theory. The resulting equations contain analytic functions with branch cuts in the complex mass squared plane. Therefore the minimum of the effective action may lie in the complex mass squared plane. Many solutions to these equations can be found on the second, third, etc. Riemann sheets of the equation, though their physical interpretation is not clear. Our results and the established properties of the S-matrix in general, and of the N/D solutions in particular, guide us to the correct choice of the Riemann sheet. We count the number of states and find only one in each spin-parity and isospin channel with quantum numbers corresponding to the fields in the Lagrangian, i....e., to Castillejo-Dalitz-Dyson (CDD) poles. We examine the numerical solutions in both the strong and weak coupling regimes and calculate the Kallen-Lehmann spectral densities and then use them for physical interpretation. (C) 2002 Elsevier Science B.V. All rights reserved.
Извор:
Nuclear Physics A, 2003, 713, 1-2, 133-147
DOI: 10.1016/S0375-9474(02)01293-9
ISSN: 0375-9474
WoS: 000179523800008
Scopus: 2-s2.0-0037433873
Колекције
Институција/група
VinčaTY - JOUR AU - Nakamura, I AU - Dmitrasinovic, V PY - 2003 UR - https://vinar.vin.bg.ac.rs/handle/123456789/2587 AB - We show an explicit connection between the solution to the equations of motion in the Gaussian functional approximation [I. Nakamura, V. Dmitrasinovic, Prog. Theor. Phys. 106 (2001) 11951 and the minimum of the (Gaussian) effective potential/action of the linear Sigma model, as well as with the N/D method in dispersion theory. The resulting equations contain analytic functions with branch cuts in the complex mass squared plane. Therefore the minimum of the effective action may lie in the complex mass squared plane. Many solutions to these equations can be found on the second, third, etc. Riemann sheets of the equation, though their physical interpretation is not clear. Our results and the established properties of the S-matrix in general, and of the N/D solutions in particular, guide us to the correct choice of the Riemann sheet. We count the number of states and find only one in each spin-parity and isospin channel with quantum numbers corresponding to the fields in the Lagrangian, i.e., to Castillejo-Dalitz-Dyson (CDD) poles. We examine the numerical solutions in both the strong and weak coupling regimes and calculate the Kallen-Lehmann spectral densities and then use them for physical interpretation. (C) 2002 Elsevier Science B.V. All rights reserved. T2 - Nuclear Physics A T1 - Linear Sigma model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action VL - 713 IS - 1-2 SP - 133 EP - 147 DO - 10.1016/S0375-9474(02)01293-9 ER -
@article{ author = "Nakamura, I and Dmitrasinovic, V", year = "2003", abstract = "We show an explicit connection between the solution to the equations of motion in the Gaussian functional approximation [I. Nakamura, V. Dmitrasinovic, Prog. Theor. Phys. 106 (2001) 11951 and the minimum of the (Gaussian) effective potential/action of the linear Sigma model, as well as with the N/D method in dispersion theory. The resulting equations contain analytic functions with branch cuts in the complex mass squared plane. Therefore the minimum of the effective action may lie in the complex mass squared plane. Many solutions to these equations can be found on the second, third, etc. Riemann sheets of the equation, though their physical interpretation is not clear. Our results and the established properties of the S-matrix in general, and of the N/D solutions in particular, guide us to the correct choice of the Riemann sheet. We count the number of states and find only one in each spin-parity and isospin channel with quantum numbers corresponding to the fields in the Lagrangian, i.e., to Castillejo-Dalitz-Dyson (CDD) poles. We examine the numerical solutions in both the strong and weak coupling regimes and calculate the Kallen-Lehmann spectral densities and then use them for physical interpretation. (C) 2002 Elsevier Science B.V. All rights reserved.", journal = "Nuclear Physics A", title = "Linear Sigma model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action", volume = "713", number = "1-2", pages = "133-147", doi = "10.1016/S0375-9474(02)01293-9" }
Nakamura, I.,& Dmitrasinovic, V.. (2003). Linear Sigma model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action. in Nuclear Physics A, 713(1-2), 133-147. https://doi.org/10.1016/S0375-9474(02)01293-9
Nakamura I, Dmitrasinovic V. Linear Sigma model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action. in Nuclear Physics A. 2003;713(1-2):133-147. doi:10.1016/S0375-9474(02)01293-9 .
Nakamura, I, Dmitrasinovic, V, "Linear Sigma model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action" in Nuclear Physics A, 713, no. 1-2 (2003):133-147, https://doi.org/10.1016/S0375-9474(02)01293-9 . .