Convergent expansion about mean field theory I. The expansion

doi:https://doi.org/10.1016/0003-4916(76)90026-9

Title: Convergent expansion about mean field theory I. The expansion

Full Record
Other Related Research

Abstract

A convergent expansion in the multiphase region is given for nearly Gaussian quantum field theory. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. The ground state of the P (phi)/sub 2/= (lambdaphi/sup 4/-phi/sup 2/-..mu..phi)/sub 2/ model is studied, with mod ..mu.. < or =lambda/sup 2/very-much-less-than1. The ground state is close to the classical free field, obtained by replacing P (phi) by the quadratic mean field polynomial P/sub c/(phi), tangent to P at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. Analyticity is established in lambda for ..mu..=0 in the sector Imlambda

Authors:: Glimm, J; Jaffe, A; Spencer, T

Publication Date:: 1976-10-01

Research Org.:: Rockefeller University, New York, New York 10021

OSTI Identifier:: 7134730

Resource Type:: Journal Article

Journal Name:: Ann. Phys. (N.Y.); (United States)

Additional Journal Information:: Journal Volume: 101:2

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; SERIES EXPANSION; ISING MODEL; PERTURBATION THEORY; PHASE TRANSFORMATIONS; SOLITONS; VACUUM STATES; CRYSTAL MODELS; FIELD THEORIES; MATHEMATICAL MODELS; QUASI PARTICLES; 645400* - High Energy Physics- Field Theory

Citation Formats


                    Glimm, J, Jaffe, A, and Spencer, T. Convergent expansion about mean field theory I. The expansion.  United States: N. p., 1976. 
        Web.  doi:10.1016/0003-4916(76)90026-9.

Copy to clipboard


                    Glimm, J, Jaffe, A, & Spencer, T. Convergent expansion about mean field theory I. The expansion.  United States.  https://doi.org/10.1016/0003-4916(76)90026-9

Copy to clipboard


                    Glimm, J, Jaffe, A, and Spencer, T. Fri .  
        "Convergent expansion about mean field theory I. The expansion".  United States.  https://doi.org/10.1016/0003-4916(76)90026-9.

Copy to clipboard


                    
@article{osti_7134730,

  title        = {Convergent expansion about mean field theory I. The expansion},

  author       = {Glimm, J and Jaffe, A and Spencer, T},

  abstractNote = {A convergent expansion in the multiphase region is given for nearly Gaussian quantum field theory. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. The ground state of the P (phi)/sub 2/= (lambdaphi/sup 4/-phi/sup 2/-..mu..phi)/sub 2/ model is studied, with mod ..mu.. < or =lambda/sup 2/very-much-less-than1. The ground state is close to the classical free field, obtained by replacing P (phi) by the quadratic mean field polynomial P/sub c/(phi), tangent to P at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. Analyticity is established in lambda for ..mu..=0 in the sector Imlambda},

  doi          = {10.1016/0003-4916(76)90026-9},

  url          = {https://www.osti.gov/biblio/7134730},
  journal      = {Ann. Phys. (N.Y.); (United States)},
number       = ,

  volume       = 101:2,

  place        = {United States},

  year         = {1976},

  month        = {10}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1016/0003-4916(76)90026-9

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Convergence of lattice approximations and infinite volume limit in the (lambdaphi/sup 4/-sigmaphi/sup 2/-. mu. phi)/sub 3/ field theory

Journal Article Park, Y M - J. Math. Phys. (N.Y.); (United States)

By unified method we prove the convergence of the lattice approximation of the (lambdaphi/sup 4/-sigmaphi/sup 2/-..mu..phi)/sub 3/ field model with periodic, Dirichlet and Neumann boundary conditions in a finite box. This then allows us to take the inifinite volume limit of the Dirichlet states by Nelson's monotonicity argument. The model under consideration satisfies all the Wightman axioms except possibly the uniqueness of the vacuum for ..mu..=0 and the mass gap.
https://doi.org/10.1063/1.523277
Verification of axioms for Euclidean and relativistic fields and Haag's theorem in a class of P(phi)$sub 2$-models

Journal Article Froehlich, J - Ann. Inst. Henri Poincare, Sect. A, v. 21, no. 4, pp. 271-317

Axioms for Euclidean (Bose) fields are proposed and shown to suffice for the reconstruction of relativistic quantum fields satisfying the Wightman axioms. Those axioms are verified for a class of P(phi)$sub 2$ models. They seem to provide a suitable framework for (Bose) field theories in two and three space- time dimensions. It is shown that the P(phi)$sub 2$-interacting field in the infinite volume limit is not a (generalized) free field or a wick polynomial of a (generalized) free field. If P$sub 1$ and P$sub 2$ are two interaction polynomials in the region of convergence of the Glimm-Jaffe-Spencer cluster expansion thenmore »« less
Functional differential equation approach to the large N expansion and mean field perturbation theory

Journal Article Bender, C M ; Cooper, F - Ann. Phys. (N.Y.); (United States)

An apparent difference between formulating mean field perturbation theory for lambdaphi/sup 4/ field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi/sup 4/ field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equationsmore »« less
https://doi.org/10.1016/0003-4916(85)90147-2
Operator-product expansion and the asymptotic behavior of spontaneously broken scalar field theories

Journal Article Taylor, C ; McClain, B - Phys. Rev. D; (United States)

We reexamine a recent study of the operator-product expansion in spontaneously broken scalar field theories. First, the asymptotic behavior of the propagator in a spontaneously broken lambdaphi/sup 4/ theory is calculated to lowest nontrivial order. The use of the operator-product expansion in the ''naive'' vacuum, with operators developing nonvanishing vacuum expectation values, is found to correctly reproduce the usual perturbative analysis of the shifted theory when carried out to the same order. The renormalization-group improvement of this result is studied. We find that ..gamma..2, the renormalization-group coefficient of the operator phi/sup 2/, is nonzero at first order in lambda. Thismore »« less
https://doi.org/10.1103/PhysRevD.28.1364
Mass eigenfunction expansions for the relativistic Kepler problem and arbitrary static magnetic field in relativistic quantum theory

Journal Article Hostler, L C - J. Math. Phys. (N.Y.); (United States)

We investigate the existence of orthogonality and completeness relations for the eigenvalue problem associated with the differential operator ..lambda.. = -Pi/sub ..mu../Pi/sub ..mu../ -iesigma x (E+iB), Pi/sub ..mu../ = -i partial/sub ..mu../-eA/sub ..mu../. The operator ..lambda.. acts on 2 x 1 Pauli-type spinor fields defined over all Minkowski space, and may be interpreted as the square of the mass of a charged Dirac particle moving in an external c-number electromagnetic field. We show that ..lambda.. is self-adjoint with respect to the not positive-definite inner product (phi/sub b/; phi/sub a/) = ..integral.. d/sup 4/x phi-bar/sub b/phi/sub a/, where phi-bar/sub b/ ismore »« less
https://doi.org/10.1063/1.526791

Similar Records