Physics
Scientific paper
Nov 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phrvd..36.3114c&link_type=abstract
Physical Review D (Particles and Fields), Volume 36, Issue 10, 15 November 1987, pp.3114-3127
Physics
112
Lagrangian And Hamiltonian Approach, Renormalization, Particle-Theory And Field-Theory Models Of The Early Universe
Scientific paper
We derive the time-evolution equations appropriate to initial-value problems in λ(φαφα)2 field theory at large N. The Heisenberg equations of motion for this theory are compared to the Schrödinger equation for a wave functional constrained to be in a Gaussian state [the time-dependent Hartree-Fock (TDHF) ansatz]. The TDHF ansatz corresponds to a special choice of initial conditions for the general large-N Heisenberg equations of motion. The renormalization of the theory is discussed in both approaches and a simple method is given to arrive at finite differential equations suitable for numerical integration forward in time. A necessary and sufficient general condition for these equations to be finite is that the initial state contain a finite average number of particles and/or correlated particle pairs per unit volume.
Cooper Fred
Mottola Emil
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