## Abstract

A method of summing diagrams in quantum field theory beyond the variational Gaussian approximation is proposed using the continuum form of the recently developed plaquette expansion. In the context of {lambda} {phi}{sup 4} theory the Hamiltonian, H [{phi}], of Schroedinger functional equation H [{phi}] {Psi} [{phi}] = E {Psi} [{phi}] can be written down in tri-diagonal form as a cluster expansion in terms of connected moment coefficients derived from Hamiltonian moments with respect to a trial state V{sub 1} [{phi}]. The usual variational procedure corresponds to minimizing the zeroth order of this cluster expansion. At first order in the expansion the Hamiltonian in this form can be diagonalized analytically. the subsequent expression for the vacuum energy E contains Hamiltonian moments up to fourth order and hence is a summation over multi-loop diagrams laying the foundation for the calculation of the effective potential beyond the Gaussian approximation. 7 refs., 1 tab.

## Citation Formats

Hollenberg, L C.L.
Beyond the variational principle in quantum field theory.
Australia: N. p.,
1994.
Web.

Hollenberg, L C.L.
Beyond the variational principle in quantum field theory.
Australia.

Hollenberg, L C.L.
1994.
"Beyond the variational principle in quantum field theory."
Australia.

@misc{etde_10114020,

title = {Beyond the variational principle in quantum field theory}

author = {Hollenberg, L C.L.}

abstractNote = {A method of summing diagrams in quantum field theory beyond the variational Gaussian approximation is proposed using the continuum form of the recently developed plaquette expansion. In the context of {lambda} {phi}{sup 4} theory the Hamiltonian, H [{phi}], of Schroedinger functional equation H [{phi}] {Psi} [{phi}] = E {Psi} [{phi}] can be written down in tri-diagonal form as a cluster expansion in terms of connected moment coefficients derived from Hamiltonian moments with respect to a trial state V{sub 1} [{phi}]. The usual variational procedure corresponds to minimizing the zeroth order of this cluster expansion. At first order in the expansion the Hamiltonian in this form can be diagonalized analytically. the subsequent expression for the vacuum energy E contains Hamiltonian moments up to fourth order and hence is a summation over multi-loop diagrams laying the foundation for the calculation of the effective potential beyond the Gaussian approximation. 7 refs., 1 tab.}

place = {Australia}

year = {1994}

month = {Dec}

}

title = {Beyond the variational principle in quantum field theory}

author = {Hollenberg, L C.L.}

abstractNote = {A method of summing diagrams in quantum field theory beyond the variational Gaussian approximation is proposed using the continuum form of the recently developed plaquette expansion. In the context of {lambda} {phi}{sup 4} theory the Hamiltonian, H [{phi}], of Schroedinger functional equation H [{phi}] {Psi} [{phi}] = E {Psi} [{phi}] can be written down in tri-diagonal form as a cluster expansion in terms of connected moment coefficients derived from Hamiltonian moments with respect to a trial state V{sub 1} [{phi}]. The usual variational procedure corresponds to minimizing the zeroth order of this cluster expansion. At first order in the expansion the Hamiltonian in this form can be diagonalized analytically. the subsequent expression for the vacuum energy E contains Hamiltonian moments up to fourth order and hence is a summation over multi-loop diagrams laying the foundation for the calculation of the effective potential beyond the Gaussian approximation. 7 refs., 1 tab.}

place = {Australia}

year = {1994}

month = {Dec}

}