By Volker Dietrich, Klaus Habetha, Gerhard Jank

ISBN-10: 0792350375

ISBN-13: 9780792350378

Clifford Algebras is still a fast-growing self-discipline, with ever-increasing purposes in lots of clinical fields. This quantity comprises the lectures given on the Fourth convention on Clifford Algebras and their functions in Mathematical Physics, held at RWTH Aachen in may well 1996. The papers characterize an very good survey of the most recent advancements round Clifford research and its purposes to theoretical physics. viewers: This booklet should still attract physicists and mathematicians operating in parts related to features of advanced variables, associative earrings and algebras, essential transforms, operational calculus, partial differential equations, and the arithmetic of physics.

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Clifford Algebras is still a fast-growing self-discipline, with ever-increasing purposes in lots of medical fields. This quantity comprises the lectures given on the Fourth convention on Clifford Algebras and their purposes in Mathematical Physics, held at RWTH Aachen in could 1996. The papers symbolize an first-class survey of the latest advancements round Clifford research and its functions to theoretical physics.

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**Extra info for Fluctuations, information, gravity and the quantum potential**

**Example text**

This method for generating quantum fractals basically involves (given s) choosing a quantum number, say n, and then considering the series that contains its powers n = nr . There is also another related method (cf. [142]) of generating quantum fractals based on the presence of discontinuities in the wave function. The emergence of fractal features arises from the perturbations that such discontinuities cause in the wave function during propagation. 2) and sum over n from 1 to N; the quantum fractal is then obtained in the limit N → ∞.

Indeed as indicated in [316, 317] (working in a relativistic context but this should hold in general) one expects space time uncertainty relations even at a semiclassical level since any localization experiment will generate a gravitational ﬁeld and deform spacetime. Thus there are relations [qµ , qν ] = iλ2P Qµν where λP is the Planck length and the picture of spacetime as a local Minkowski manifold should break down at distances of order λP . One wants the localization experiment to avoid creating a black hole (putting the object out of “reach”) for example 3 and this suggests ∆x0 ( 1 ∆xi ) λ2P with ∆x1 ∆x2 + ∆x2 ∆x3 + ∆x3 ∆x1 λ2P (cf.

Deﬁne (f real valued) 1 f (t ± ) − f (t) ✷ f i ; (f ) = (∇+ + ∇− )f − (∇+ − ∇− f ); ± ✷t 2 2 1 i a ,j (t) = [(∆+ x)j − (−1)j (∆− x)j ] − [(∆+ x)j + (−1)j (∆− x)j ] 2 2 Here one assumes h > 0 and (f, h) ≥ > 0 where (f, h) is the minimal resolution deﬁned via inf {a (f ) < h} for a f (t) = |[f (t + ) + f (t − ) − 2f (t)]/ |. If (f, h) is not 0 then f is not diﬀerentiable (but not conversely). Now assume some minimal control over the lack of diﬀerentiability (cf. 27) ∇± f (t) = ∂f ✷ x ∂f ✷f = + + ✷t ∂t ✷t ∂x n 2 1 ∂j f a ,j (t) j j!

### Fluctuations, information, gravity and the quantum potential by Volker Dietrich, Klaus Habetha, Gerhard Jank

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