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Communications in Mathematical Physics

, Volume 64, Issue 1, pp 49–72 | Cite as

Absence of symmetry breakdown and uniqueness of the vacuum for multicomponent field theories

  • J. Bricmont
  • J. R. Fontaine
  • L. Landau
Article

Abstract

Correlation inequalities are used to show that the two component λ(φ2)2 model (with HD, D, HP, P boundary conditions) has a unique vacuum if the field does not develop a non-zero expectation value. It follows by a generalized Coleman theorem that in two space-time dimensions the vacuum is unique for all values of the coupling constant. In three space-time dimensions the vacuum is unique below the critical coupling constant.

For then-componentP(|φ|2)2+μφ1 model, absence of continuous symmetry breaking, as μ goes to zero, is proven for all states which are translation invariant, satisfy the spectral condition, and are weak* limit points of finite volume states satisfyingN loc τ and higher order estimates.

Keywords

Neural Network Nonlinear Dynamics Symmetry Breaking Finite Volume Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • J. Bricmont
    • 1
  • J. R. Fontaine
    • 1
  • L. Landau
    • 2
  1. 1.Institut de Physique ThéoriqueUniversité de LouvainLouvain-La-NeuveBelgium
  2. 2.Mathematics Department, Bedford CollegeUniversity of LondonLondonEngland

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