@article{fulp_2017, title={Spin groups of super metrics and a theorem of Rogers}, volume={111}, ISSN={["1879-1662"]}, DOI={10.1016/j.geomphys.2016.10.009}, abstractNote={We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Super metrics define reductions OSg of the relevant frame bundle. When principal bundles S˜g exist with structure group the simply connected covering group G̃ of the structure group of OSg, representations of G̃ define vector bundles associated to S˜g whose sections are “spinor fields” associated with the super metric g. Using a generalization of a Theorem of Rogers, which is itself one of the main results of this paper, we show that for super metrics we call body reducible, each such simply connected covering group G̃ is a super Lie group with a conventional super Lie algebra as its corresponding super Lie algebra. Some of our results were known to DeWitt (1984) using formal Grassmann series and others were known by Rogers using finitely many Grassmann generators and passing to a direct limit. We work exclusively in the category of G∞ supermanifolds with G∞ mappings. Our supernumbers are infinite series of products of Grassmann generators subject to convergence in the ℓ1 norm introduced by Rogers (1980, 2007).}, journal={JOURNAL OF GEOMETRY AND PHYSICS}, author={Fulp, Ronald}, year={2017}, month={Jan}, pages={40–53} }
 @article{fulp_2014, title={Infinite Dimensional DeWitt Supergroups and their Bodies}, volume={57}, ISSN={["1496-4287"]}, DOI={10.4153/cmb-2013-025-6}, abstractNote={Abstract}, number={2}, journal={CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES}, author={Fulp, Ronald}, year={2014}, month={Jun}, pages={283–288} }
 @article{cook_fulp_2011, title={HOLONOMY IN ROGERS SUPERMANIFOLDS WITH APPLICATIONS TO SUPER YANG-MILLS THEORY}, volume={8}, ISSN={["1793-6977"]}, DOI={10.1142/s0219887811005221}, abstractNote={ The present paper focuses on a certain class of Banach manifolds we call Rogers supermanifolds since they are indeed supermanifolds modeled on graded Banach spaces. Although the subject of holonomy is well-developed for superanalytic supermanifolds utilizing local ring formulations of supermanifolds this seems not to be the case for supermanifolds modeled on graded Banach manifolds in the sense of Rogers. The proof of our main result requires a partial development of these concepts for such supermanifolds. Our main result determines conditions under which a super connection on a superprincipal bundle [Formula: see text] induces a connection on a quotient superprincipal bundle [Formula: see text] where [Formula: see text] is a foliation of [Formula: see text] and [Formula: see text] is the induced foliation on [Formula: see text]. We also show how such a quotient formulation may be used to describe in a fully geometric fashion the so-called "conventional constraints" of super Yang–Mills theory. One consequence of our development is that instead of requiring two superconnections to describe Yang–Mills theory as is the case in some formulations, we describe the relevant concepts using a single superconnection and moreover we show that the "pregauge transformations" are simply ordinary gauge transformations on the appropriate quotient bundles. }, number={2}, journal={INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS}, author={Cook, James S. and Fulp, Ronald}, year={2011}, month={Mar}, pages={429–458} }
 @article{cook_fulp_2008, title={Infinite-dimensional super Lie groups}, volume={26}, ISSN={["0926-2245"]}, DOI={10.1016/j.difgeo.2008.04.009}, abstractNote={A super Lie group is a group whose operations are G ∞ mappings in the sense of Rogers. Thus the underlying supermanifold possesses an atlas whose transition functions are G ∞ functions. Moreover the images of our charts are open subsets of a graded infinite-dimensional Banach space since our space of supernumbers is a Banach Grassmann algebra with a countably infinite set of generators. In this context, we prove that if h is a closed, split sub-super Lie algebra of the super Lie algebra of a super Lie group G , then h is the super Lie algebra of a sub-super Lie group of G . Additionally, we show that if g is a Banach super Lie algebra satisfying certain natural conditions, then there is a super Lie group G such that the super Lie algebra g is in fact the super Lie algebra of G . We also show that if H is a closed sub-super Lie group of a super Lie group G , then G → G / H is a principal fiber bundle. We emphasize that some of these theorems are known when one works in the super-analytic category and also when the space of supernumbers is finitely generated in which case, one can use finite-dimensional techniques. The issues dealt with here are that our supermanifolds are modeled on graded Banach spaces and that all mappings must be morphisms in the G ∞ category.}, number={5}, journal={DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS}, author={Cook, James and Fulp, Ronald}, year={2008}, month={Oct}, pages={463–482} }
 @article{fulp_2007, title={BRST extension of geometric quantization}, volume={37}, ISSN={["0015-9018"]}, DOI={10.1007/s10701-006-9090-8}, abstractNote={Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the physics literature are more general but suffer from having states with infinite or zero "norms" and thus are not admissible as states. Also BRST operators for many systems require regularization to be well-defined. In our more restricted context, we show that our treatment does not suffer from any of these difficulties.}, number={1}, journal={FOUNDATIONS OF PHYSICS}, author={Fulp, Ronald}, year={2007}, month={Jan}, pages={103–124} }
 @article{al-ashhab_fulp_2005, title={Canonical transformations of local functionals and sh-Lie structures}, volume={53}, ISSN={["1879-1662"]}, DOI={10.1016/j.geomphys.2004.07.005}, abstractNote={In many Lagrangian field theories, there is a Poisson bracket on the space of local functionals. One may identify the fields of such theories as sections of a vector bundle. It is known that the Poisson bracket induces an sh-Lie structure on the graded space of horizontal forms on the jet bundle of the relevant vector bundle. We consider those automorphisms of the vector bundle which induce mappings on the space of functionals preserving the Poisson bracket and refer to such automorphisms as canonical automorphisms. We determine how such automorphisms relate to the corresponding sh-Lie structure. If a Lie group acts on the bundle via canonical automorphisms, there are induced actions on the space of local functionals and consequently on the corresponding sh-Lie algebra. We determine conditions under which the sh-Lie structure induces an sh-Lie structure on a corresponding reduced space where the reduction is determined by the action of the group. These results are not directly a consequence of the corresponding theorems on Poisson manifolds as none of the algebraic structures are Poisson algebras.}, number={4}, journal={JOURNAL OF GEOMETRY AND PHYSICS}, author={Al-Ashhab, S and Fulp, R}, year={2005}, month={Apr}, pages={365–391} }
 @article{fulp_2005, title={Functionals and the quantum master equation}, volume={44}, ISSN={["0020-7748"]}, DOI={10.1007/s10773-005-4832-5}, abstractNote={The quantum master equation is usually formulated in terms of functionals of the components of mappings (fields in physpeak) from a space–time manifold M into a finite-dimensional vector space. The master equation is the sum of two terms one of which is the antibracket (odd poisson bracket) of functionals and the other is the Laplacian of a functional. Both of these terms seem to depend on the fact that the mappings on which the functionals act are vector-valued. It turns out that neither the Laplacian nor the antibracket is well-defined for sections of an arbitrary vector bundle. We show that if the functionals are permitted to have their values in an appropriate graded tensor algebra whose factors are the dual of the space of smooth functions on M, then both the antibracket and the Laplace operator can be invariantly defined. This permits one to develop the Batalin–Vilkovisky approach to BRST cohomology for functionals of sections of an arbitrary vector bundle.}, number={9}, journal={INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS}, author={Fulp, RO}, year={2005}, month={Sep}, pages={1599–1616} }
 @article{fulp_lada_stasheff_2002, title={sh-Lie algebras induced by gauge transformations}, volume={231}, ISSN={["0010-3616"]}, DOI={10.1007/s00220-002-0678-3}, abstractNote={Traditionally symmetries of field theories are encoded via Lie group actions, or more generally, as Lie algebra actions. A significant generalization is required when “gauge parameters” act in a field dependent way. Such symmetries appear in several field theories, most notably in a “Poisson induced” class due to Schaller and Strobl [SS94] and to Ikeda [Ike94], and employed by Cattaneo and Felder [CF99] to implement Kontsevich's deformation quantization [Kon97]. Consideration of “particles of spin > 2” led Berends, Burgers and van Dam [Bur85,BBvD84,BBvD85] to study “field dependent parameters” in a setting permitting an analysis in terms of smooth functions. Having recognized the resulting structure as that of an sh-Lie algebra (L ∞-algebra), we have now formulated such structures entirely algebraically and applied it to a more general class of theories with field dependent symmetries.}, number={1}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Fulp, R and Lada, T and Stasheff, J}, year={2002}, month={Nov}, pages={25–43} }
 @article{barnich_fulp_lada_stasheff_2000, title={Algebra structures on Hom (C, L)}, volume={28}, ISSN={["0092-7872"]}, DOI={10.1080/00927870008827169}, abstractNote={We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C L) fail to hold. We define the concept of twisted domain (TD) algebras in order to recover the symmetries and also construct a modified Chevalley-Eilenbcrg complex in order to define the cohomology of such algebras.}, number={11}, journal={COMMUNICATIONS IN ALGEBRA}, author={Barnich, G and Fulp, R and Lada, T and Stasheff, J}, year={2000}, pages={5481–5501} }
 @article{barnich_fulp_lada_stasheff_1998, title={The sh Lie structure of Poisson brackets in field theory}, volume={191}, ISSN={["0010-3616"]}, DOI={10.1007/s002200050278}, abstractNote={A general construction of an sh Lie algebra (L ∞-algebra) from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential algebra of horizontal forms. The same construction applies for graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.}, number={3}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Barnich, G and Fulp, R and Lada, T and Stasheff, J}, year={1998}, month={Feb}, pages={585–601} }