Once again on the equivalence theorem

We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite counterterms is possible, leading to physically non-equivalent quantum theories while the equivalent theorem remains valid.Comment: 12 pages, LATEX, report number was correcte

Initial Conditions for Semiclassical Field Theory

Semiclassical approximation based on extracting a c-number classical component from quantum field is widely used in the quantum field theory. Semiclassical states are considered then as Gaussian wave packets in the functional Schrodinger representation and as Gaussian vectors in the Fock representation. We consider the problem of divergences and renormalization in the semiclassical field theory in the Hamiltonian formulation. Although divergences in quantum field theory are usually associated with loop Feynman graphs, divergences in the Hamiltonian approach may arise even at the tree level. For example, formally calculated probability of pair creation in the leading order of the semiclassical expansion may be divergent. This observation was interpretted as an argumentation for considering non-unitary evolution transformations, as well as non-equivalent representations of canonical commutation relations at different time moments. However, we show that this difficulty can be overcomed without the assumption about non-unitary evolution. We consider first the Schrodinger equation for the regularized field theory with ultraviolet and infrared cutoffs. We study the problem of making a limit to the local theory. To consider such a limit, one should impose not only the requirement on the counterterms entering to the quantum Hamiltonian but also the requirement on the initial state in the theory with cutoffs. We find such a requirement in the leading order of the semiclassical expansion and show that it is invariant under time evolution. This requirement is also presented as a condition on the quadratic form entering to the Gaussian state.Comment: 20 pages, Plain TeX, one postscript figur

Breather solution of non-linear Klein-Gordon equation

A technique for obtaining an approximate breather solution of the Klein-Gordon equation is presented. A breather solution of the equation describing the propagation of nonlinear waves in a graphene-based superlattice is investigated.Comment: 16 pages, 5 figure