Supergeometry in Locally Covariant Quantum Field Theory

Hack, Thomas-Paul; Hanisch, Florian; Schenkel, Alexander

doi:10.1007/s00220-015-2516-4

Cited by 10 publications

(27 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore one has ζ N (S)A(ψ • ρ − ) = A( S (ψ • ρ + ))A(κ + ) −1 A(κ − ) with the same morphisms κ ± as in the original application of part (i), because those morphisms obviously satisfy the characterising equation F L (ψ • υ) • F L (κ ± ) = F L (ψ • ρ ± ) and have the same codomainŨ. Combining this with (23) gives…”

Section: 1 Hypotheses Statement Of Main Results and Consequencesmentioning

confidence: 85%

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Fewster

2017

Commun. Math. Phys.

View full text Add to dashboard Cite

Abstract:The Coleman-Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions n ≥ 2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of G with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance.

show abstract

Section: 1 Hypotheses Statement Of Main Results and Consequencesmentioning

confidence: 85%

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Fewster

2017

Commun. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…We also present examples of super pseudodifferential operators which are relevant for physics, in particular the equation of motion operators (and their associated propagators) of the supergeometric field theories studied in Ref. 9. Crucially, as we have already indicated above, our concept of super principal symbols is able to detect ellipticity (or hyperbolicity) of these operators.…”

Section: Introductionmentioning

confidence: 82%

Wavefront sets and polarizations on supermanifolds

Dappiaggi

Gimperlein

Murro

et al. 2017

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

In this paper we develop the foundations for microlocal analysis on supermanifolds.Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for superdistributions which generalizes Dencker's polarization sets for vector-valued distributions to supergeometry. In particular, our super wavefront sets detect polarization information of the singularities of superdistributions. We prove a refined pullback theorem for superdistributions along supermanifold morphisms, which as a special case establishes criteria when two superdistributions may be multiplied. As an application of our framework, we study the singularities of distributional solutions of a supersymmetric field theory.

show abstract

“…This idea is based on a proposal formulated already by Schmitt in [43] which is motivated by the functorial approach to supermanifold theory according to Molotkov [37] and Sachse [39]. This approach also recently found application in the local approach to super quantum field theories (QFT) [36]. Moreover, the description of fermionic fields turns out to be quite similar to considerations in perturbative algebraic QFT [40,41].…”

Section: S-relative Super Connection Formsmentioning

confidence: 99%

“…In the following, we will adopt the terminology of [36] introducing the notion of a relative supermanifold 4 . However, unlike as in [36], in order to study fermionic fields, we will not restrict on superpoints as parametrising supermanifolds. We will then define principal connections and connection 1-forms on parametrising supermanifolds.…”

Section: S-relative Super Connection Formsmentioning

confidence: 99%

See 1 more Smart Citation

Super fiber bundles, connection forms, and parallel transport

Eder

2021

Preprint

View full text Add to dashboard Cite

The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms and their parallel transport, that ties together various approaches. We begin with a detailed introduction to super fiber bundles. We then introduce the concept of so-called relative supermanifolds as well as bundles and connections defined in these categories. Studying these objects turns out to be of utmost importance in order to, among other things, model anticommuting classical fermionic fields in mathematical physics. We then construct the parallel transport map corresponding to such connections and compare the results with those found by other means in the mathematical literature. Finally, applications of these methods to supergravity will be discussed such as the Cartan geometric formulation of Poincaré supergravity as well as the description of Killing vector fields and Killing spinors of super Riemannian manifolds arising from metric reductive super Cartan geometries. This paper can also be read as a companion paper of [24] studying a mathematical rigorous approach towards geometric supergravity.

show abstract

Supergeometry in Locally Covariant Quantum Field Theory

Cited by 10 publications

References 35 publications

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Wavefront sets and polarizations on supermanifolds

Super fiber bundles, connection forms, and parallel transport

Contact Info

Product

Resources

About