Yuriy Mishchenko Papers:
Mishchenko Y., Ji C.-R. (2005) "A novel variational approach for quantum field theory: example of study of the ground state and phase transition in nonlinear sigma model.", International Journal of Modern Physics A 20, 3488

We study here a novel approach to finding ground state of a quantum field theory. Ground state is the quantum state of a field theory that minimizes its energy, E[H]. Since quantum state is, in general, a functional, such optimization, in general, is very difficult. In some cases, E[H] can be decomposed into a sum of fairly simple expectations. An obvious example - E[H]=E[K]+E[V], where K is kinetic energy term, and V is the potential. The essence of this work is to solve variational problem in terms of this expectation values after finding a set of constraints they should satisfy. I.e., instead of solving variational functional problem, solve min A + B, where A and B are simply numbers, A=E[K], B=E[V], satisfying constraints C(A,B)=0 established by analyzing (E[K],E[V]) for all possible quantum states. Here, this approach is applied to studying nonlinear sigma model. Full text