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Spin-Field Correspondence

Institute of Physics, Jagiellonian University, ul. ojasiewicza 11, 30-348 Kraków, Poland
Universe 2017, 3(2), 29; https://doi.org/10.3390/universe3020029
Received: 4 January 2017 / Revised: 15 March 2017 / Accepted: 21 March 2017 / Published: 23 March 2017
(This article belongs to the Special Issue Varying Constants and Fundamental Cosmology)
In the recent article Phys. Lett. B 2016, 759, 424–429, a new class of field theories called Nonlinear Field Space Theory was proposed. In this approach, the standard field theories are considered as linear approximations to some more general theories characterized by nonlinear field phase spaces. The case of spherical geometry is especially interesting due to its relation with the spin physics. Here, we explore this possibility, showing that classical scalar field theory with such a field space can be viewed as a perturbation of a continuous spin system. In this picture, the spin precession and the scalar field excitations are dual descriptions of the same physics. The duality is studied in the example of the Heisenberg model. It is shown that the Heisenberg model coupled to a magnetic field leads to a non-relativistic scalar field theory, characterized by quadratic dispersion relation. Finally, on the basis of analysis of the relation between the spin phase space and the scalar field theory, we propose the Spin-Field correspondence between the known types of fields and the corresponding spin systems. View Full-Text
Keywords: nonlinear field space theory; spin systems; Heisenberg model; quantum gravity nonlinear field space theory; spin systems; Heisenberg model; quantum gravity
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Mielczarek, J. Spin-Field Correspondence. Universe 2017, 3, 29.

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