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Particles in the superworldline and BRST

Eugenia Boffo (2022)

Archivum Mathematicum

In this short note we discuss N -supersymmetric worldlines of relativistic massless particles and review the known result that physical spin- N / 2 fields are in the first BRST cohomology group. For N = 1 , 2 , 4 , emphasis is given to particular deformations of the BRST differential, that implement either a covariant derivative for a gauge theory or a metric connection in the target space seen by the particle. In the end, we comment about the possibility of incorporating Ramond-Ramond fluxes in the background.

Positive energy quantization of linear dynamics

Jan Dereziński, Christian Gérard (2010)

Banach Center Publications

The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into three stages: the description of a classical system, the algebraic quantization and the Hilbert space quantization. Four kinds of systems are distinguished: neutral bosonic, neutral bosonic, charged bosonic and charged fermionic. The formalism that is described follows closely the usual constructions employed in quantum physics to introduce noninteracting quantum...

Properties of non-hermitian quantum field theories

Carl M. Bender (2003)

Annales de l’institut Fourier

In this paper I discuss quantum systems whose Hamiltonians are non-Hermitian but whose energy levels are all real and positive. Such theories are required to be symmetric under 𝒞 𝒫 𝒯 , but not symmetric under 𝒫 and 𝒯 separately. Recently, quantum mechanical systems having such properties have been investigated in detail. In this paper I extend the results to quantum field theories. Among the systems that I discuss are - φ 4 and i φ 3 theories. These theories all have unexpected and remarkable properties. I discuss...

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