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Localization in Relativistic Quantum Theories

Herrmann, Lars Oliver (2010) Localization in Relativistic Quantum Theories. [Preprint]

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    Although the concept of localization in non-relativistic quantum mechanics is mathematically well-defined there is no obvious and unambiguous way to generalize it to relativistic quantum theory. After a brief review of localization in quantum mechanics the Newton-Wigner localization scheme is introduced and it is shown by the example of a massive spinless system how it leads to a position operator with seemingly unphysical properties. This motivated the development of several theorems which claim to rule out the existence of localizable particles. A particularly important one of them is presented and its validity discussed. In the last section however it is shown that if localization is considered with respect to spacelike hyperplanes, the properties of the Newton-Wigner position operators are not necessarily unphysical and localizable particles can exist.

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    Item Type: Preprint
    Additional Information: This essay was submitted as part of the required work for the Masters Level course, Part III, in the Department of Applied Mathematics and Theoretical Physics, Cambridge University, May 2010.
    Keywords: Newton-Wigner localization hyperplane-dependence
    Subjects: Specific Sciences > Physics
    Specific Sciences > Physics > Quantum Field Theory
    Depositing User: Lars Oliver Herrmann
    Date Deposited: 20 Jun 2010
    Last Modified: 07 Oct 2010 11:19
    Item ID: 5427

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