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01-07-2016

Effects of a scalar scaling field on quantum mechanics

Author: Paul Benioff

Published in: Quantum Information Processing | Issue 7/2016

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Abstract

This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at each location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. The lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.

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Equivalents means strings with an arbitrary number of \(a's\) added to the right and left ends of the string.

There is another representation of \(\bar{V}^{t}_{s}\) in which the vectors do not scale. This is \(\bar{V}^{t}_{s}=\{V,\pm _{s},(s/t)\cdot _{s},(t/s)|f_{s}|_{s}, f_{s}\}.\) This is not used here because the equivalence between n- dimensional vector spaces and \(\bar{C}^{n}\) (or \(\bar{R}^{n}\)) fails for this \(\bar{V}^{t}_{s}\). \(\bar{V}^{t}_{s}\) is not equivalent to \((\bar{C}^{n})^{t}_{s}\) or to \((\bar{R}^{n})^{t}_{s}.\))

The same result as in Eq. 52 can be obtained by taking the derivative of \({\hbox {e}}^{\gamma _{x}(z)}\psi (z)\) in the fiber at x.

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Title: Effects of a scalar scaling field on quantum mechanics
Author: Paul Benioff
Publication date: 01-07-2016
Publisher: Springer US
Published in: Quantum Information Processing / Issue 7/2016
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-016-1312-1

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