# Convergent expansion about mean field theory I. The expansion

## 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:

- Publication Date:

- 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.

```
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

```
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.
```

```
@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}

}