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  • 1.
    Atanasiu, Dragu
    et al.
    Högskolan i Borås, Akademin för textil, teknik och ekonomi.
    Bengtsson, Anders
    Högskolan i Borås, Akademin för textil, teknik och ekonomi.
    Modern differential- och integralkalkyl2015 (uppl. 1)Bok (Refereegranskat)
  • 2.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    A Riccati type PDE for light-front higher helicity vertices2014Ingår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 9, nr 105Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 3.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    A visit to Skidmore college, Saratoga Springs, New York, 20042005Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This report tells the story of my visit to Skidmore College, Saratoga Springs, New York. I went there as a STINT1 ”Excellence in Teaching” fellow during the fall semester of the academic year 2004.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 4.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    An Abstract Interface to Higher Spin Field Theory2005Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, nr 4Artikel i tidskrift (Refereegranskat)
  • 5.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    BRST theory for continuous spin2013Ingår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 108, nr 10Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 6.
    Bengtsson, Anders
    Högskolan i Borås, Akademin för textil, teknik och ekonomi.
    Investigations into light-front interactions for massless fields (I): Non-constructibility of higher spin quartic amlplitudes2016Ingår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 12, s. 134-, artikel-id 134Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 7.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Kan ingenjörsmatematik undervisas effektivt utgående från en humanistisk syn på matematiken?2013Konferensbidrag (Övrigt vetenskapligt)
    Abstract [sv]

    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.

  • 8.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Light-front higher-helicity interactions2012Ingår i: Fortschritte der Physik. Special Issue: Proceedings of the XVIIthe European Workshop on String Theory 2011, Padua, Italy, 4-9 September 2011 (part 2), Wiley , 2012, s. 1038-1043Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

  • 9.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Matematik som bildningsämne i högskolan2011Ingår i: Det goda lärandet / [ed] Anders Burman, Patrik Mehrens, Studentlitteratur , 2011, s. 147-166Kapitel i bok, del av antologi (Övrigt vetenskapligt)
  • 10.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Mechanical Models for Higher Gauge Fields2009Ingår i: Fortschritte der Physik, ISSN 0015-8208, E-ISSN 1521-3978, Vol. 57, nr 5-7, s. 499-504Artikel i tidskrift (Refereegranskat)
  • 11.
    Bengtsson, Anders
    Högskolan i Borås, Akademin för textil, teknik och ekonomi.
    Notes on Cubic and Quartic Light-Front KinematicsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    The purpose of this short note is to collect a set of formulas pertaining to momentum kinematics for higher spin light-front vertices. At least one of the formulas seems to be previously unknown.

  • 12.
    Bengtsson, Anders
    Högskolan i Borås, Akademin för textil, teknik och ekonomi.
    Quartic amplitudes for Minkowski higher spin2016Ingår i: Higher Spin Gauge Theories / [ed] Lars Brink, Marc Henneaux, Mikhael A Vasiliev, Singapore: World Scientific, 2016, s. 353-370Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 13.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Structure of Higher Spin Gauge Interactions2007Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, nr 7Artikel i tidskrift (Refereegranskat)
  • 14.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Systematics of Higher-spin Light-front Interactions2012Ingår i: arXivArtikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    The original cubic interaction terms for higher spin gauge fields in four dimensions and their reformulation using Fock space vertex operators is reviewed. As a new result, the complete list of all cubic vertex functions in D=4 is derived. It is observed, contrary to what would have been expected, that the non-linear dynamical Poincar\'e transformations do not restrict the cubic interactions beyond what is required by kinematics. The role of the SU(1,1) algebra of tracelessness constraints is clarified. It is shown that higher spin fields couple non-minimally to gravity at the cubic level in D=4 light-front dynamics. Based on a detailed analysis of the structure of the light-front Poincar\'e algebra, the formalism is then generalized to all orders in the interaction. The interacting theory, being a deformation of the free theory, takes the form of a strongly homotopy Lie algebra. It is conjectured that the ensuing recursive equations, if they can be explicitly solved, will encode all interaction data into a denumerable set of functions of p+, the overall transverse momentum structure being fixed already at the kinematical level.

  • 15.
    Bengtsson, Anders
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Towards unifying structures in higher spin gauge symmetry2008Ingår i: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 4Artikel i tidskrift (Övrig (populärvetenskap, debatt, mm))
    Abstract [en]

    This article is expository in nature, outlining some of the many still incompletely understood features of higher spin field theory. We are mainly considering higher spin gauge fields in their own right as free-standing theoretical constructs and not circumstances where they occur as part of another system. Considering the problem of introducing interactions among higher spin gauge fields, there has historically been two broad avenues of approach. One approach entails gauging a non-Abelian global symmetry algebra, in the process making it local. The other approach entails deforming an already local but Abelian gauge algebra, in the process making it non-Abelian. In cases where both avenues have been explored, such as for spin 1 and 2 gauge fields, the results agree (barring conceptual and technical issues) with Yang-Mills theory and Einstein gravity. In the case of an infinite tower of higher spin gauge fields, the first approach has been thoroughly developed and explored by M. Vasiliev, whereas the second approach, after having lain dormant for a long time, has received new attention by several authors lately. In the present paper we briefly review some aspects of the history of higher spin gauge fields as a backdrop to an attempt at comparing the gauging vs. deforming approaches. A common unifying structure of strongly homotopy Lie algebras underlying both approaches will be discussed. The modern deformation approach, using BRST-BV methods, will be described as far as it is developed at the present time. The first steps of a formulation in the categorical language of operads will be outlined. A few aspects of the subject that seems not to have been thoroughly investigated are pointed out.

  • 16.
    Bengtsson, Anders
    et al.
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Arlebrink, Jim
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Desaix, Mats
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Försöksprojekt i matematik vid Ingenjörshögskolan i Borås2002Rapport (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 17.
    Bengtsson, Anders
    et al.
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Brink, Lars
    Kim, Sung-Soo
    Counterterms in gravity in the light-front formulation and a D = 2 conformal-like symmetry in gravity2013Ingår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 118, nr 3Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 18.
    Bengtsson, Anders
    et al.
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Brink, Lars
    Kim, Sung-Soo
    Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Summetry in Gravity2013Ingår i: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 2013, nr 3Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 19.
    Bengtsson, Anders K. H.
    et al.
    Högskolan i Borås, Institutionen Ingenjörshögskolan.
    Holfve Sabel, Mary-Anne
    Högskolan i Borås, Institutionen för Pedagogik.
    Applications of eigenvector centrality to small social networksManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    This article investigates conceptual and methodological questions that may arise in applying eigenvector centrality to small social networks such as school classes. The focus on small networks brings out surprising and subtle properties related to the interpretation of the measure. We investigate examples where the weighted adjacency matrix of the underlying social network quantifies inter-individual preferences of whom to work with or play with. We show that mathematical operations such as transposition and symmetrization of the weighted adjacency matrix enhances the power of the measure. It is demonstrated that it is not sufficient to work with the original weight matrix. By working with a symmetrized or a semi-symmetrized or a transposed weight matrix different characteristics of the social interaction are revealed. The method chosen depends on the purpose of the investigation. Identifying isolated or popular individuals in the network are also facilitated using these operations.

    Ladda ner fulltext (pdf)
    fulltext
1 - 19 av 19
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