Nonperturbative calculation of symmetry breaking in quantum field theory

A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the expectation value of the scalar field to first order in delta, where delta is a measure of the degree of nonlinearity in the interaction term.

field theory: scalar
symmetry breaking
nonperturbative
perturbation theory: delta expansion
path integral

References(23)

Figures(0)

A NEW PERTURBATIVE APPROACH TO NONLINEAR PROBLEMS

Carl M. Bender
(
- Washington U., St. Louis
)
,
Kimball A. Milton
(
- Oklahoma U.
)
,
Stephen S. Pinsky
(
- Ohio State U.
)
,
L.M. Simmons, Jr.
(
- Los Alamos
)

- J.Math.Phys. 30 (1989) 1447
•
DOI:
- 10.1063/1.528326

A New perturbative approach to nonlinear partial differential equations

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•
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- 10.1063/1.529047

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LOGARITHMIC APPROXIMATIONS TO POLYNOMIAL LAGRANGIANS

Carl M. Bender
(
- Imperial Coll., London
)
,
K.A. Milton
(
- Oklahoma U.
)
,
M. Moshe
(
- Kyoto U.
)
,
S.S. Pinsky
(
- Ohio State U.
)
,
L.M. Simmons
(
- Los Alamos
)

- Phys.Rev.Lett. 58 (1987) 2615-2618,
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•
DOI:
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Novel Perturbative Scheme in Quantum Field Theory

Carl M. Bender
(
- Washington U., St. Louis
)
,
Kimball A. Milton
(
- Oklahoma U.
)
,
Moshe Moshe
(
- Technion
)
,
Stephen S. Pinsky
(
- Ohio State U.
)
,
L.M. Simmons, Jr.
(
- Los Alamos
)

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•
DOI:
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A New Nonperturbative Calculation: Renormalization and the Triviality of $\lambda \phi^4$ in Four-dimensions Field Theory

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•
DOI:
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TRIVIALITY OF MONOMIAL HIGGS POTENTIALS

Hing Tong Cho
(
- Oklahoma U. and
- Ohio State U.
)
,
Kimball A. Milton
(
- Oklahoma U. and
- Ohio State U.
)
,
James M. Cline
(
- Ohio State U.
)
,
Stephen S. Pinsky
(
- Ohio State U.
)
,
L.M. Simmons, Jr.
(
- Los Alamos and
- Santa Fe Inst.
)

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•
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A NEW PERTURBATIVE APPROXIMATION APPLIED TO SUPERSYMMETRIC QUANTUM FIELD THEORY

Carl M. Bender
(
- Washington U., St. Louis
)
,
Kimball A. Milton
(
- Oklahoma U.
)
,
Stephen S. Pinsky
(
- Ohio State U.
)
,
L.M. Simmons, Jr.
(
- Arizona U. and
- Los Alamos
)

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•
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A New Perturbative Calculation of the Fermion - Boson Mass Ratio in a Supersymmetric Quantum Field Theory

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•
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The $\Delta$ Expansion and Local Gauge Invariance

Carl M. Bender
(
- Washington U., St. Louis
)
,
F. Cooper
(
- Brown U. and
- Los Alamos
)
,
K.A. Milton
(
- Ohio State U. and
- Oklahoma U.
)

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•
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Delta expansion applied to quantum electrodynamics

- Phys.Rev.D 45 (1992) 639-653
•
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Delta expansion for local gauge theories. 1. A One-dimensional model

Carl M. Bender
(
- Washington U., St. Louis
)
,
Fred Cooper
(
- Los Alamos
)
,
Kimball A. Milton
(
- Oklahoma U.
)
,
Moshe Moshe
(
- Washington U., St. Louis
)
,
Stephen S. Pinsky
(
- Ohio State U.
)

et al.

- Phys.Rev.D 45 (1992) 1248-1260
•
DOI:
- 10.1103/PhysRevD.45.1248

The Delta expansion for local gauge theories. 2. Nonperturbative calculation of the anomaly in the Schwinger model

Carl M. Bender
(
- Washington U., St. Louis
)
,
Kimball A. Milton
(
- Oklahoma U.
)
,
Moshe Moshe
(
- Washington U., St. Louis
)

- Phys.Rev.D 45 (1992) 1261-1275
•
DOI:
- 10.1103/PhysRevD.45.1261

The $\Delta$ Expansion for Stochastic Quantization

Carl M. Bender
(
- Washington U., St. Louis
)
,
F. Cooper
(
- Brown U. and
- Los Alamos
)
,
K.A. Milton
(
- Ohio State U. and
- Oklahoma U.
)

- Phys.Rev.D 39 (1989) 3684-3689
•
DOI:
- 10.1103/PhysRevD.39.3684

Novel perturbation expansion for the Langevin equation

Carl M. Bender
(
- Washington U., St. Louis
)
,
Fred Cooper
(
- Los Alamos
)
,
L.M. Simmons, Jr.
(
- Santa Fe Inst.
)
,
Pinaki Roy
(
- Indian Statistical Inst., Calcutta
)
,
Greg Kilcup
(
- Ohio State U.
)

- J.Statist.Phys. 64 (1991) 395-428
•
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- 10.1007/BF01057884

HOT DELTA EXPANSION

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•
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- 10.1103/PhysRevD.41.3269

- Nuovo Cim.A 22 454

EFFECT OF RENORMALIZATION ON THE LARGE ORDER BEHAVIOR OF WEAK AND STRONG COUPLING PERTURBATION THEORY

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- Phys. Rev. D25 ( 1982) 427-433
•
DOI:
- 10.1103/PhysRevD.25.427

Nonunique Solution to the Schwinger-dyson Equations

Carl M. Bender
(
- Washington U., St. Louis
)
,
F. Cooper
(
- Los Alamos
)
,
L.M. Simmons
(
- Los Alamos
)

- Phys.Rev.D 39 (1989) 2343-2349,
- LOS ALAMOS NAT. LAB. - LA-UR-88-3519 (88,REC.JAN.89) 21p,
- Phys. Rev. D39 (1989) 2343-2349 AND LOS ALAMOS NAT. LAB. - LA-UR-88-3519 (88,REC.JAN.89) 21p
•
DOI:
- 10.1103/PhysRevD.39.2343

Analytic continuation of Eigenvalue problems

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•
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- 10.1016/0375-9601(93)90153-Q

- Sov.Phys.JETP 67 230

Quantal Problems With Partial Algebraization of the Spectrum

Mikhail A. Shifman
(
- Moscow, ITEP
)
,
A.V. Turbiner
(
- Moscow, ITEP
)

- Commun.Math.Phys. 126 (1989) 347
•
DOI:
- 10.1007/BF02125129

Bender-Dunne orthogonal polynomials and quasiexact solvability

e-Print:
- hep-th/9601088