The Vacuum Structure of Light-Front $\ddot{I}{•}_{1+1}^4$-Theory

Abstract

We discuss the vacuum structure of $\ddot{I}{•}^4$-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 $\ddot{I}•$ 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.

28 pages LaTeX, 1 Postscript figure