1995/12/21 by T. Heinzl, Christian Stern, C. Stern +2 · 3 citations
Mathematics · Physics and Astronomy · #Ansatz #Black Holes and Theoretical Physics #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Field (mathematics) #Field theory (psychology) #Geometry #Higgs boson #Mathematical physics #Mathematics #Operator (biology) #Perturbation theory (quantum mechanics) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Theoretical physics #Vacuum expectation value #Vacuum state #Zero mode #hep-ph #hep-th
paper · pdf · doi:10.1007/bf02909165
published in The European Physical Journal C 72(1), 353-364 (Springer Science+Business Media) · 28 pages LaTeX, 1 Postscript figure
arxiv created 1995/12/21 · openalex publication_date 1996/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss the vacuum structure of ϕ4-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 ϕ 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.