BRST model for equivariant cohomology and representatives for the equivariant Thom class Export

@article{citeulike:488178, abstract = { One of the fundamental properties of (cohomological) topological field theories is the presence of a nilpotent operator, the BRST operator, whose cohomology models that of some moduli space (of connections in the case of gauge theories). The original space of fields being infinite-dimensional, this is achieved by choosing the BRST operator to be a coboundary operator for equivariant cohomology on the space of fields with respect to some infinite-dimensional symmetry group of automorphisms (gauge transformations). While this interpretation of the BRST operator in topological field theories has, in one way or another, been known for some time, this article, which can also be read as a clear and concise introduction to the algebraic aspects of equivariant cohomology per se, makes this connection much more precise. <P> In particular, in a finite-dimensional context, the "BRST model" is shown to be one member of a one-parameter family connecting the classical Cartan and Weil models for equivariant cohomology. Furthermore, using the concept of "Fourier transform of differential forms", the author shows how to obtain the equivariant Mathai-Quillen representative of the Thom class \ref[V. Mathai and D. G. Quillen, Topology <strong>25</strong> (1986), no. 1, 85--110; <A HREF="/msnmain?fn=105\&fmt=doc\&r=1\&pg1=CNO\&s1=836726\&loc=fromrevtext">MR0836726 (87k:58006)</A>] as the Fourier transform of a simple BRST closed element, thus connecting BRST cohomology with the interpretation of topological field theory given by M. F. Atiyah and L. C. Jeffrey \ref[J. Geom. Phys. <strong>7</strong> (1990), no. 1, 119--136; <A HREF="/msnmain?fn=105\&fmt=doc\&r=1\&pg1=CNO\&s1=1094734\&loc=fromrevtext">MR1094734 (92f:58025)</A>].}, author = {Kalkman, Jaap}, citeulike-article-id = {488178}, citeulike-linkout-0 = {http://www.ams.org/mathscinet-getitem?mr=1218928}, journal = {Comm. Math. Phys.}, keywords = {brst, cohomology, equivariant, thom\_class, tqft}, mrnumber = {MR1218928}, number = {3}, pages = {447--463}, posted-at = {2006-02-01 01:53:18}, priority = {2}, title = {BRST model for equivariant cohomology and representatives for the equivariant Thom class}, url = {http://www.ams.org/mathscinet-getitem?mr=1218928}, volume = {153}, year = {1993} }

TY - JOUR ID - citeulike:488178 L3 - citeulike-article-id:488178 N2 - One of the fundamental properties of (cohomological) topological field theories is the presence of a nilpotent operator, the BRST operator, whose cohomology models that of some moduli space (of connections in the case of gauge theories). The original space of fields being infinite-dimensional, this is achieved by choosing the BRST operator to be a coboundary operator for equivariant cohomology on the space of fields with respect to some infinite-dimensional symmetry group of automorphisms (gauge transformations). While this interpretation of the BRST operator in topological field theories has, in one way or another, been known for some time, this article, which can also be read as a clear and concise introduction to the algebraic aspects of equivariant cohomology per se, makes this connection much more precise. <P> In particular, in a finite-dimensional context, the "BRST model" is shown to be one member of a one-parameter family connecting the classical Cartan and Weil models for equivariant cohomology. Furthermore, using the concept of "Fourier transform of differential forms", the author shows how to obtain the equivariant Mathai-Quillen representative of the Thom class \ref[V. Mathai and D. G. Quillen, Topology <strong>25</strong> (1986), no. 1, 85--110; <A HREF="/msnmain?fn=105&fmt=doc&r=1&pg1=CNO&s1=836726&loc=fromrevtext">MR0836726 (87k:58006)</A>] as the Fourier transform of a simple BRST closed element, thus connecting BRST cohomology with the interpretation of topological field theory given by M. F. Atiyah and L. C. Jeffrey \ref[J. Geom. Phys. <strong>7</strong> (1990), no. 1, 119--136; <A HREF="/msnmain?fn=105&fmt=doc&r=1&pg1=CNO&s1=1094734&loc=fromrevtext">MR1094734 (92f:58025)</A>]. IS - 3 JF - Comm. Math. Phys. EP - 463 TI - BRST model for equivariant cohomology and representatives for the equivariant Thom class VL - 153 SP - 447 KW - brst KW - cohomology KW - equivariant KW - thom_class KW - tqft AU - Kalkman, Jaap PY - 1993/// UR - http://www.ams.org/mathscinet-getitem?mr=1218928 ER -