The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion areobtained as total differential equations in many variables. It is shown that if the system is integrable, one can obta...The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion areobtained as total differential equations in many variables. It is shown that if the system is integrable, one can obtain thecanonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any needto introduce unphysical auxiliary fields. As an example we quantize the O(2) nonlinear sigma model using two differentapproaches: the functional Schrodinger method to obtain the wave functionals for the ground and the exited state andthen we quantize the same model using the canonical path integral quantization as an integration over the canonicalphase-space coordinates.展开更多
Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ - T phase diagra...Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ - T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the BoseEinstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.展开更多
文摘The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion areobtained as total differential equations in many variables. It is shown that if the system is integrable, one can obtain thecanonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any needto introduce unphysical auxiliary fields. As an example we quantize the O(2) nonlinear sigma model using two differentapproaches: the functional Schrodinger method to obtain the wave functionals for the ground and the exited state andthen we quantize the same model using the canonical path integral quantization as an integration over the canonicalphase-space coordinates.
文摘Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ - T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the BoseEinstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.
