Perturbative - nonperturbative connection in quantum mechanics and field theory

On the occasion of this ArkadyFest, celebrating Arkady Vainshtein's 60th birthday, I review some selected aspects of the connection between perturbative and nonperturbative physics, a subject to which Arkady has made many important contributions. I first review this connection in quantum mechanics, which was the subject of Arkady's very first paper. Then I discuss this issue in relation to effective actions in field theory, which also touches on Arkady's work on operator product expansions. Finally, I conclude with a discussion of a special quantum mechanical system, a quasi-exactly solvable model with energy-reflection duality, which exhibits an explicit duality between the perturbative and nonperturbative sectors, without invoking supersymmetry.

Note:

17 pp, 9 figures; Review talk at ArkadyFest Symposium, May 2002, Minneapolis

talk: Minneapolis 2002/05/17
perturbation theory
nonperturbative
quantum mechanics
potential
ground state
energy levels
quantum electrodynamics
effective action
operator product expansion

References(44)

Figures(9)

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(
- Cornell U., LNS
)

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An example of a divergent perturbation expansion in field theory

Charles Angas Hurst
(
- Cambridge U.
)

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Charles Angas Hurst
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Walter E. Thirring

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Divergence of Perturbation Expansion

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Anharmonic oscillator

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(
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)
,
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(
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)

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(
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)
,
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(
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)

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Carl M. Bender
(
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)
,
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(
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)
,
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(
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)

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Carl M. Bender
(
- Washington U., St. Louis
)
,
E. Weniger
(
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)

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(
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)
,
G. Parisi
(
- IHES, Bures-sur-Yvette
)
,
Jean Zinn-Justin
(
- Saclay
)

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CALCULATION OF INSTANTON - ANTI-INSTANTON CONTRIBUTIONS IN QUANTUM MECHANICS

E.B. Bogomolny
(
- Landau Inst.
)

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OPERATOR EXPANSION IN QUANTUM CHROMODYNAMICS BEYOND PERTURBATION THEORY

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Consequences of Dirac's theory of positrons

W. Heisenberg
(
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)
,
H. Euler
(
- Leipzig U.
)

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On gauge invariance and vacuum polarization

Julian S. Schwinger
(
- Harvard U.
)

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