O(2)model in polar coordinates at nonzero temperature

Abstract

We study the restoration of spontaneously broken symmetry at nonzero temperature in the framework of the O(2) model using polar coordinates. We apply the CJT formalism to calculate the masses and the condensate in the double-bubble approximation, both with and without a term that explicitly breaks the O(2) symmetry. We find that, in the case with explicitly broken symmetry, the mass of the angular degree of freedom becomes tachyonic above a temperature of about 300 MeV. Taking the term that explicitly breaks the symmetry to be infinitesimally small, we find that the Goldstone theorem is respected below the critical temperature. However, this limit cannot be performed for temperatures above the phase transition. We find that, no matter whether we break the symmetry explicitly or not, there is no region of temperature in which the radial and the angular degree of freedom become degenerate in mass. These results hold also when the mass of the radial mode is sent to infinity.

Effects of renormalizing the chiral SU(2) quark-meson model

“…[23][24][25], and for the mesonic fields with works from refs. [26][27][28][29]. In the combined approach we compare our results with the work from ref.…”

Symmetry-improved CJT effective action

“…In particular, for the case of global O(N ) symmetries that we will be studying here, a naive truncation of the CJT effective action violates the Goldstone theorem [7,8] by higher-order terms, giving rise to a massive Goldstone boson in the Spontaneous Symmetry Breaking (SSB) phase of the theory [9][10][11][12]. Thus far, several studies have been presented in the literature, attempting to provide a satisfactory solution to this problem [11][12][13][14][15][16][17][18][19][20].…”

“…Finally, there has been an attempt to formulate the CJT effective action using a non-linear representation of the background fields in polar coordinates [20]. This approach predicts a massless Goldstone boson, but it suffers from non-analyticities that restrict the domain of validity of the theory at high temperatures.…”

Implications of the fermion vacuum term in the extended SU(3) quark meson model on compact star properties

“…Since QCD can not be solved on the lattice at nonzero density, effective models are needed to study the features and interactions of high density matter [5,[19][20][21][22][23]. The chiral SU(3) quark meson model is a well established and studied framework [5,[23][24][25][26][27][28][29][30][31][32][33][34]. Its advantage in comparison to other chiral models like the Nambu-Jona-Lasinio model [35][36][37][38] lies in its renormalizability [31,32,39] by taking into account vacuum fluctuations.…”