The Vacuum Structure of Light-Front $φ^4_{1+1}$-Theory

Details The Vacuum Structure of Light-Front $φ^4_{1+1}$-Theory The Vacuum Structure of Light-Front $φ^4_{1+1}$-Theory

1995-12-21

arxiv.org/abs/hep-th/9512179v1

Z.Phys. C72 (1996) 353-364

Physics

High Energy Physics

High Energy Physics - Theory

28 pages LaTeX, 1 Postscript figure

Scientific paper

10.1007/BF02909165

We discuss the vacuum structure of $\phi^4$-theory in 1+1 dimensions quantised on the light-front $x^+ =0$. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having longitudinal light-front momentum equal to zero, as a function of all the other modes in the theory. We analyse whether this zero mode can lead to a non-vanishing vacuum expectation value of the field $\phi$ and thus to spontaneous symmetry breaking. In perturbation theory, we get no symmetry breaking. If we solve the constraint, however, non-perturbatively, within a mean-field type Fock ansatz, the situation changes: while the vacuum state itself remains trivial, we find a non-vanishing vacuum expectation value above a critical coupling. Exactly the same result is obtained within a light-front Tamm-Dancoff approximation, if the renormalisation is done in the correct way.

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