These notes contain — apart from some physics — scattered reminiscences of everyday life at the Institute for Theoretical Physics in Göteborg in the early eighties. The text has been in the making for many years. Some of it was written inspired by the Lars Brink 70-fest at The Solvay Institute in Brussels in 2014, but was never finished or published. Parts of the old text have now been replaced by a review of the quite unexpected recent renaissance for light-front higher spin theory. Lars sadly did not live to experience more than the very beginnings of this quite remarkable development.

The dynamical commutators of the light-front Poincar{\'e} algebra yield first order differential equations in the $p^+$ momenta for the interaction vertex operators. The homogeneous solution to the equation for the quartic vertex is studied. Consequences as regards the constructibility assumption of quartic higher spin amplitudes from cubic amplitudes are discussed. The existence of quartic contact interactions unrelated to cubic interactions by Poincar{\'e} symmetry indicates that the higher spin S-matrix is not constructible. Thus quartic amplitude based no-go results derived by BCFW recursion for Minkowski higher spin massless fields may be circumvented.

The old problem of finding general quartic interaction terms between fields of higher helicities on the light-front is discussed from the point of view of calculating the corresponding amplitudes directly from the cubic vertices using BCFW recursion. Amplitude based no-go results that has appeared in the literature are reviewed and discussed and it is pointed out how they may perhaps be circumvented.

This paper is based on a curious observation about an equation related to the tracelessness constraints of higher spin gauge fields. A similar equation also occurs in the theory of continuous spin representations of the Poincaré group. Expressed in an oscillator basis for the higher spin fields, the equation becomes a non-linear partial differential operator of the Riccati type acting on the vertex functions. The consequences of the equation for the cubic vertex is investigated in the light-front formulation of higher spin theory. The vertex is fixed by the PDE up to a set of terms that can be considered as boundary data for the PDE. These terms can serve as off-shell quantum corrections. In order to set the present work in perspective, some comments and comparisons to recent research on higher spin interactions are made. A few particular cubic vertices are calculated explicitly and compared to similar results in the literature, in particular the interesting cases 2 ÿ 3 ÿ 3 and 3 ÿ 2 ÿ 2 involving spin 2 fields.

Some puzzling aspects of higher spin field theory in Minkowski space-time, such as the tracelessness constraints and the search for an underlying physical principle, are discussed. A connecting idea might be provided by the recently much researched continuous spin representations of the Poincaré group. The Wigner equations, treated as first class constraints, yields to a four-constraint BRST formulation. The resulting field theory, generalizing free higher spin field theory, is one among a set of higher spin theories that can be related to previous work on unconstrained formulations. In particular, it is conjectured that the unconstrained higher spin theory of Francia and Sagnotti is a limit of a continuous spin theory. Furthermore, a simple analysis of the constraint structure reveals a hint of a physical rationale behind the trace constraints.

In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincaré invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N = 8 Supergravity should work.

In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity should work.

Matematikämnet i ungdomsskolan står i fokus för diskussioner, fortbildning och reformarbete sedan flera år. Iväntan på att förkunskaperna hos våra inkommande ingenjörsstudenter förbättras, vad kan vi som högskolelärare göra? Här argumenteras för ett angreppssätt som inte prövats i någon större utsträckning: Undervisa matematiken som en humanism och inte som ett hjälpämne till naturvetenskap och teknik; att ta de humanistiska aspekterna på matematiken som fundament för undervisningsmetoder och kursdesign. Detta kan skapa möjligheter att på allvar fokusera begreppsmässiga svårigheter samtidigt som exempel på matematikens tillämpningar inom teknik och samhälle kan moderniseras.

The reformulation, using Fock space vertex operators, of the original light-front cubic interaction terms for higher spin gauge fields is reviewed with comments on quantum higher spin gravity. The formalism is generalized to all orders in the interaction. The ensuing recursive equations for the higher order vertices, if they can be explicitly solved, will encode all interaction data into a denumerable set of rational functions of p+, the overall transverse momentum structure being fixed already at the kinematical level. A more thorough exposition can be found in the archive.