arXiv subjects

Devashish Singh

Publications and source records attributed to Devashish Singh.

3 recordsLinked to original sources

arXiv2020

Actions for twisted spectral triple and the transition from the Euclidean to the Lorentzian

This is a review of recent results regarding the application of Connes' noncommutative geometry to the Standard Model, and beyond. By twisting (in the sense of Connes-Moscovici) the spectral triple of the Standard Model, one does not only get an extra scalar field which stabilises the electroweak vacuum, but also an unexpected 1-form field. By computing the fermionic action, we show how this field induces a transition from the Euclidean to the Lorentzian signature. Hints on a twisted version of the spectral action are also briefly mentioned.

math-ph↗

arXiv2020

Twisting Noncommutative Geometries with Applications to High Energy Physics

With the bare essentials of noncommutative geometry (defined by a spectral triple), we first describe how it naturally gives rise to gauge theories. Then, we quickly review the notion of twisting (in particular, minimally) noncommutative geometries and how it induces a Wick rotation, that is, a transition of the metric signature from euclidean to Lorentzian. We focus on comparatively more tractable examples of spectral triples; such as the ones corresponding to a closed Riemannian spin manifold, $U(1)$ gauge theory, and electrodynamics. By minimally twisting these examples and computing their associated fermionic actions, we demonstrate how to arrive at physically relevant actions (such as the Weyl and Dirac actions) in Lorentz signature, even though starting from euclidean spectral triples. In the process, not only do we extract a physical interpretation of the twist, but we also capture exactly how the Wick rotation takes place at the level of the fermionic action.

math-ph↗

arXiv2019

Lorentzian fermionic action by twisting euclidean spectral triples

We show how the twisting of spectral triples induces a transition from an euclidean to a lorentzian noncommutative geometry, at the level of the fermionic action. More specifically, we compute the fermionic action for the twisting of a closed euclidean manifold, then that of a two-sheet euclidean manifold, and finally the twisting of the spectral triple of electrodynamics in euclidean signature. We obtain the Weyl and the Dirac equations in lorentzian signature (and in the temporal gauge). The twisted fermionic action is then shown to be invariant under an action of the Lorentz group. This permits to interprete the field of 1-form that parametrizes the twisted fluctuation of a manifold as the (dual) of the energy momentum 4-vector.

math-ph↗