Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2003-01-10
Phys.Rev. D68 (2003) 105014
Physics
High Energy Physics
High Energy Physics - Phenomenology
Revtex, 32 pages; substantial new material dealing with non-equilibrium evolution beyond Hartree approx. based on the LvN form
Scientific paper
10.1103/PhysRevD.68.105014
We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to obtain the correlation functions both in and beyond the Hartree approximation, for the quantum mechanical analog of the $\phi^{4}$ model. The technique involves representing the Hamiltonian in a Fock basis of annihilation and creation operators. By separating it into a solvable Gaussian part involving quadratic terms and a perturbation of quartic terms, it is possible to find the improved vacuum state to any desired order. The correlation functions for the field theory are then investigated in the Hartree approximation and those beyond the Hartree approximation are obtained by finding the improved vacuum state corrected up to ${\cal O}(\lambda^2)$. These correlation functions take into account next-to-leading and next-to-next-to-leading order effects in the coupling constant. We also use the Heisenberg formalism to obtain the time evolution equations for the equal-time, connected correlation functions beyond the leading order. These equations are derived by including the connected 4-point functions in the hierarchy. The resulting coupled set of equations form a part of infinite hierarchy of coupled equations relating the various connected n-point functions. The connection with other approaches based on the path integral formalism is established and the physical implications of the set of equations are discussed with particular emphasis on thermalization.
Khanna Faqir C.
Kim Sang Pyo
Sengupta Supratim
No associations
LandOfFree
Nonequilibrium Evolution of Correlation Functions: A Canonical Approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonequilibrium Evolution of Correlation Functions: A Canonical Approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonequilibrium Evolution of Correlation Functions: A Canonical Approach will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-231417