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The effective potential as an energy density: The one phase region

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Abstract

An explicit formula is given relating the effective potential in a finite volumeP(φ)2 quantum field theory to the expected energy density under the constraint of a fixed average filed. In the one phase region, i.e., where the classical potential equals its convex hull and has nonvanishing second derivative, it is shown via a central limit theorem that in the infinite volume limit the effective potential is equal to the constrained energy density, provided ħ is sufficiently small.

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References

  1. Cassandro, M., Jona-Lasinio, G.: Critical point behavior and probability theory. Adv. Phys.27, 913–941 (1978)

    Google Scholar 

  2. Coleman, S.: Secret symmetry. In: Laws of hadronic matter, proceedings of the eleventh course. International School of Physics Ettore Majorana. Zichichi, A. (ed.) New York: Academic Press 1975

    Google Scholar 

  3. Dimock, J.: Asymptotic perturbation expansion in theP(φ)2 quantum field theory. Commun. Math. Phys.35, 347–356 (1974)

    Google Scholar 

  4. Eckmann, J.-P.: Remarks on the classical limit of quantum field theories. Lett. Math. Phys.1, 387–394 (1977)

    Google Scholar 

  5. Fröhlich, J., Simon, B.: Pure states for generalP(φ)2 theories: construction, regularity and variational equality, Ann. Math.105, 493–526 (1977)

    Google Scholar 

  6. Fukuda, R., Kyriakopoulos, E.: Derivation of the effective potential. Nucl. Phys.B85, 354–364 (1975)

    Google Scholar 

  7. Glimm, J., Jaffe, A., Spencer, T.: A convergent expansion about mean field theory I, II. Ann. Phys.101, 610–669 (1976)

    Google Scholar 

  8. Guerra, F., Rosen, L., Simon, B.: Boundary conditions for theP(φ)2 Euclidean quantum field theory. Ann. Inst. H. Poincaré25, 231–334 (1976)

    Google Scholar 

  9. Jona-Lasinio, G.: Large fluctuations of random fields and renormalization group: Some perspectives. In: Scaling and self-similarity in physics. Fröhlich, J. (ed.) Boston, Basel, Stuttgart: Birkhäuser 1983

    Google Scholar 

  10. Schulman, L.: Magnetization probabilities and metastability in the Ising model. J. Phys. A: Math. Gen.13, 237–250 (1980)

    Google Scholar 

  11. Slade, G.: The loop expansion for the effective potential in theP(φ)2 quantum field theory. Commun. Math. Phys.102, 425–462 (1985)

    Google Scholar 

  12. Spencer, T.: The mass gap for theP(φ)2 quantum field model with a strong external field. Commun. Math. Phys.44, 143–164 (1975)

    Google Scholar 

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  1. Department of Mathematics, University of Virginia, 22903, Charlottesville, VA, USA

    Gordon Slade

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  1. Gordon Slade
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Communicated by K. Osterwalder

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Slade, G. The effective potential as an energy density: The one phase region. Commun.Math. Phys. 104, 573–580 (1986). https://doi.org/10.1007/BF01211065

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  • DOI: https://doi.org/10.1007/BF01211065

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