A cluster expansion in field theory

1982 ◽  
Vol 23 (1) ◽  
pp. 141-144
Author(s):  
James Kowall ◽  
H. M. Fried
Keyword(s):  
Field Theory ◽  
Cluster Expansion

U=∞ HUBBARD MODEL: TOWARDS THE EXACT SOLUTION IN d=∞

1989 ◽  
Vol 03 (12) ◽  
pp. 2149-2157
Author(s):  
Václav Janiš
Keyword(s):  
Field Theory ◽  
Exact Solution ◽  
External Field ◽  
Integral Representation ◽  
Hubbard Model ◽  
Cluster Expansion ◽  
Degrees Of Freedom ◽  
Exact Expression ◽  
Inhomogeneous Field ◽  
Quartic Interaction

We investigate the U=∞ Hubbard model. Using a Grassmann-integral representation, we transform this model to a Grassmann field theory with two degrees of freedom per site and with a local quartic interaction. An external inhomogeneous field is introduced so that the linked-cluster expansion be applicable. All 1-loop contributions from this expansion are summed up and an exact expression for the inhomogeneous grandcanonical potential dependent on the auxiliary external field in d=∞ is found.

scholarly journals THREE-LOOP CALCULATION OF THE ANYONIC FULL CLUSTER EXPANSION

1993 ◽  
Vol 08 (34) ◽  
pp. 3291-3299 ◽  
Author(s):  
R. EMPARAN ◽  
M.A. VALLE BASAGOITI
Keyword(s):  
Field Theory ◽  
Cluster Expansion ◽  
Cluster Coefficient ◽  
Second Order ◽  
Coupling Constant ◽  
Perturbative Correction ◽  
Chern Simons

We calculate the perturbative correction to every cluster coefficient of a gas of anyons through second order in the anyon coupling constant, as described by Chern-Simons field theory.

scholarly journals Beyond the Variational Principle in Quantum Field Theory

1995 ◽  
Vol 48 (1) ◽  
pp. 39
Author(s):  
Lloyd CL Hollenberg
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cluster Expansion ◽  
Vacuum Energy ◽  
Gaussian Approximation ◽  
Diagonal Form ◽  
Quantum Field ◽  
Zeroth Order ◽  
First Order ◽  
The Continuum

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 >-<j} theory the Hamiltonian, H[�], of the Schrodinger functional equation H[�]\II[�] = E\II[�] can be written down in tri-diagonal form as a cluster expansion in terms of connected moment coefficients derived from Hamiltonian moments (Hn) == !V�VI[�]Hn[�JVd�] with respect to a trial state VI [�]. The usual variational procedure corresponds to minimising the zeroth order of this cluster expansion. At first order in the expansion, the Hamiltonian in this form can be diagonalised 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.

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