Quantum Dynamics: Models and Mathematics pp 167-175 | Cite as

# An Asymptotic Perturbation Expansion for Multiphase \( \varphi _2^4 \cdot \)

## Abstract

We consider the d=2 quantum field, with interaction density \(
P\left( x \right) = \lambda x^4 - \frac{3} {4}x^2 .
\) for λ < < 1, this model is known to have a phase transition [1], i.e. there exist at least two different field theories for a given λ. The new result we announce here is a detailed investigation of the two theories in which ⌽ is concentrated near ± (8λ)^{-1/2}, namely the global minima of P(x). (Presumably these are the only pure states for the model.) We give a convergent expansion about the mean field approximation, which is asymptotic in powers of λ^{1/2}. We explain these ideas in more detail.

## Keywords

Gaussian Measure Cluster Expansion Path Space Interaction Density Convergent Expansion## Preview

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## References

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