We describe a duality transformation in a cosmological model of four time and four space dimensions ((4 + 4)-dimensions). In particular, we show that via the Fourier transform, at the level of the zero-point energy of...We describe a duality transformation in a cosmological model of four time and four space dimensions ((4 + 4)-dimensions). In particular, we show that via the Fourier transform, at the level of the zero-point energy of quantum mechanics and the de Sitter space, a Gaussian distribution in four dimensions leads to a dual Gaussian distribution also in four dimensions, with duality transformation <span style="white-space:nowrap;"><img src="Edit_f657c3a7-4f4c-413f-8331-632f8ffca641.png" alt="" /></span><span style="white-space:nowrap;"></span>, in the standard deviation <span style="white-space:nowrap;">σ</span>. Moreover, we show that as a consequence of such a duality in <span style="white-space:nowrap;">σ</span> a duality of the cosmological constant <span style="white-space:nowrap;">Λ</span> can be obtained. Finally, we comment on the possibility that both the oriented matroid theory as well as the surreal number theory are related to the formalism presented in this work.展开更多
文摘We describe a duality transformation in a cosmological model of four time and four space dimensions ((4 + 4)-dimensions). In particular, we show that via the Fourier transform, at the level of the zero-point energy of quantum mechanics and the de Sitter space, a Gaussian distribution in four dimensions leads to a dual Gaussian distribution also in four dimensions, with duality transformation <span style="white-space:nowrap;"><img src="Edit_f657c3a7-4f4c-413f-8331-632f8ffca641.png" alt="" /></span><span style="white-space:nowrap;"></span>, in the standard deviation <span style="white-space:nowrap;">σ</span>. Moreover, we show that as a consequence of such a duality in <span style="white-space:nowrap;">σ</span> a duality of the cosmological constant <span style="white-space:nowrap;">Λ</span> can be obtained. Finally, we comment on the possibility that both the oriented matroid theory as well as the surreal number theory are related to the formalism presented in this work.
