On a certain chain of algebras on a Hilbert sphere

1971 ◽  
Vol 5 (1) ◽  
pp. 72-73 ◽  
Author(s):  
A. S. Nemirovskii
Keyword(s):  
Hilbert Sphere

Shorter Notes: A Note on Levy's Brownian Process on the Hilbert Sphere

1972 ◽  
Vol 33 (1) ◽  
pp. 207
Author(s):  
Peggy Tang Strait
Keyword(s):  
Brownian Process ◽  
Hilbert Sphere

Strictly positive definite kernels on the hilbert sphere

1994 ◽  
Vol 55 (1-2) ◽  
pp. 91-101 ◽  
Author(s):  
Valdir A. Menegatto
Keyword(s):  
Positive Definite ◽  
Positive Definite Kernels ◽  
Hilbert Sphere

Positive definite kernels on the complex Hilbert sphere

1982 ◽  
Vol 180 (3) ◽  
pp. 193-201 ◽  
Author(s):  
Jens Peter Reus Christensen ◽  
Paul Ressel
Keyword(s):  
Positive Definite ◽  
Positive Definite Kernels ◽  
Hilbert Sphere

scholarly journals Isotropic Gaussian Processes on the Hilbert Sphere

1980 ◽  
Vol 8 (6) ◽  
pp. 1093-1106 ◽  
Author(s):  
Simeon M. Berman
Keyword(s):  
Gaussian Processes ◽  
Hilbert Sphere

scholarly journals The ABC of Physics

2021 ◽  
Vol 3 (1) ◽  
pp. 9
Author(s):  
John Skilling ◽  
Kevin Knuth
Keyword(s):  
Quantum Theory ◽  
Gaussian Distribution ◽  
Complex Numbers ◽  
Time And Space ◽  
Fundamental Object ◽  
Pauli Matrices ◽  
Hilbert Sphere

Why quantum? Why spacetime? We find that the key idea underlying both is uncertainty. In a world lacking probes of unlimited delicacy, our knowledge of quantities is necessarily accompanied by uncertainty. Consequently, physics requires a calculus of number pairs and not only scalars for quantity alone. Basic symmetries of shuffling and sequencing dictate that pairs obey ordinary component-wise addition, but they can have three different multiplication rules. We call those rules A, B and C. “A” shows that pairs behave as complex numbers, which is why quantum theory is complex. However, consistency with the ordinary scalar rules of probability shows that the fundamental object is not a particle on its Hilbert sphere but a stream represented by a Gaussian distribution. “B” is then applied to pairs of complex numbers (qubits) and produces the Pauli matrices for which its operation defines the space of four vectors. “C” then allows integration of what can then be recognised as energy-momentum into time and space. The picture is entirely consistent. Spacetime is a construct of quantum and not a container for it.

scholarly journals A note on Lévy’s Brownian process on the Hilbert sphere

1972 ◽  
Vol 33 (1) ◽  
pp. 207-207
Author(s):  
Peggy Tang Strait
Keyword(s):  
Brownian Process ◽  
Hilbert Sphere
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