The main object of this thesis is the analysis and the quantization of spinning particle
models which employ extended ”one dimensional supergravity” on the worldline, and their
relation to the theory of higher spin fields (HS).
In the first part of this work we have described the classical theory of massless spinning
particles with an SO(N) extended supergravity multiplet on the worldline, in flat and more
generally in maximally symmetric backgrounds. These (non)linear sigma models describe,
upon quantization, the dynamics of particles with spin N/2.
Then we have analyzed carefully the quantization of spinning particles with SO(N)
extended supergravity on the worldline, for every N and in every dimension D. The physical
sector of the Hilbert space reveals an interesting geometrical structure: the generalized higher
spin curvature (HSC). We have shown, in particular, that these models of spinning particles
describe a subclass of HS fields whose equations of motions are conformally invariant at the
free level; in D = 4 this subclass describes all massless representations of the Poincar´e group.
In the third part of this work we have considered the one-loop quantization of SO(N)
spinning particle models by studying the corresponding partition function on the circle.
After the gauge fixing of the supergravity multiplet, the partition function reduces to an
integral over the corresponding moduli space which have been computed by using orthogonal
polynomial techniques.
Finally we have extend our canonical analysis, described previously for flat space, to
maximally symmetric target spaces (i.e. (A)dS background). The quantization of these
models produce (A)dS HSC as the physical states of the Hilbert space; we have used an
iterative procedure and Pochhammer functions to solve the differential Bianchi identity in
maximally symmetric spaces.
Motivated by the correspondence between SO(N) spinning particle models and HS gauge
theory, and by the notorious difficulty one finds in constructing an interacting theory for fields
with spin greater than two, we have used these one dimensional supergravity models to study
and extract informations on HS.
In the last part of this work we have constructed spinning particle models with sp(2) R
symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.
| Identifer | oai:union.ndltd.org:unibo.it/oai:amsdottorato.cib.unibo.it:843 |
| Date | 19 May 2008 |
| Creators | Latini, Emanuele <1978> |
| Contributors | Bastianelli, Fiorenzo |
| Publisher | Alma Mater Studiorum - Università di Bologna |
| Source Sets | Università di Bologna |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, PeerReviewed |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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