Forschungsinitiativen
https://www.repo.unihannover.de/handle/123456789/13
Frei zugängliche Publikationen aus den Forschungsinitiativen
Fri, 25 Jun 2021 08:23:22 GMT
20210625T08:23:22Z

Composites and categories of euclidean Jordan algebras
https://www.repo.unihannover.de/handle/123456789/10816
Composites and categories of euclidean Jordan algebras
Barnum, Howard; Graydon, Matthew A.; Wilce, Alexander
We consider possible nonsignaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct daggercompact categories of such models. We show that no such composite has the exceptional Jordan algebra as a direct summand, nor does any such composite exist if one factor has an exceptional summand, unless the other factor is a direct sum of onedimensional Jordan algebras (representing essentially a classical system). Moreover, we show that any composite of simple, nonexceptional EJAs is a direct summand of their universal tensor product, sharply limiting the possibilities. These results warrant our focussing on concrete Jordan algebras of hermitian matrices, i.e., euclidean Jordan algebras with a preferred embedding in a complex matrix algebra. We show that these can be organized in a natural way as a symmetric monoidal category, albeit one that is not compact closed. We then construct a related category InvQM of embedded euclidean Jordan algebras, having fewer objects but more morphisms, that is not only compact closed but daggercompact. This category unifies finitedimensional real, complex and quaternionic mixedstate quantum mechanics, except that the composite of two complex quantum systems comes with an extra classical bit. Our notion of composite requires neither tomographic locality, nor preservation of purity under tensor product. The categories we construct include examples in which both of these conditions fail. In such cases, the information capacity (the maximum number of mutually distinguishable states) of a composite is greater than the product of the capacities of its constituents. © 2020 FahrenHouse. All rights reserved.
Wed, 01 Jan 2020 00:00:00 GMT
https://www.repo.unihannover.de/handle/123456789/10816
20200101T00:00:00Z

Perturbative linearization of supersymmetric YangMills theory
https://www.repo.unihannover.de/handle/123456789/10796
Perturbative linearization of supersymmetric YangMills theory
Ananth, Sudarshan; Lechtenfeld, Olaf; Malcha, Hannes; Nicolai, Hermann; Pandey, Chetan; Pant, Saurabh
Supersymmetric gauge theories are characterized by the existence of a transformation of the bosonic fields (Nicolai map) such that the Jacobi determinant of the transformation equals the product of the MatthewsSalamSeiler and FaddeevPopov determinants. This transformation had been worked out to second order in the coupling constant. In this paper, we extend this result (and the framework itself) to third order in the coupling constant. A diagrammatic approach in terms of tree diagrams, aiming to extend this map to arbitrary orders, is outlined. This formalism bypasses entirely the use of anticommuting variables, as well as issues concerning the (non)existence of offshell formulations for these theories. It thus offers a fresh perspective on supersymmetric gauge theories and, in particular, the ubiquitous N = 4 theory. © 2020, The Author(s).
Wed, 01 Jan 2020 00:00:00 GMT
https://www.repo.unihannover.de/handle/123456789/10796
20200101T00:00:00Z

Nonunitary evolution in the general extended EFT of inflation & excited initial states
https://www.repo.unihannover.de/handle/123456789/4929
Nonunitary evolution in the general extended EFT of inflation & excited initial states
Ashoorioon, Amjad
I study the general case that arises in the Extended Effective Field Theory of Inflation (gEEFToI), in which the coefficients of the sixth order polynomial dispersion relation depend on the physical wavelength of the fluctuation mode, hence they are timedependent. At arbitrarily short wavelengths the unitarity is lost for each mode. Depending on the values of the gEEFToI parameters in the unitary gauge action, two scenarios can arise: in one, the coefficients of the polynomial become singular, flip signs at some physical wavelength and asymptote to a constant value as the wavelength of the mode is stretched to infinity. Starting from the WKB vacuum, the twopoint function is essentially singular in the infinite IR limit. In the other case, the coefficients of the dispersion relation evolve monotonically from zero to a constant value in the infinite IR. In order to have a finite power spectrum starting from the vacuum in this case, the mode function has to be an eigensolution of the Confluent Heun (CH) equation, which leads to a very confined parameter space for gEEFToI. Finally, I look at a solution of the CH equation which is regular in the infinite IR limit and yields a finite power spectrum in either scenario. I demonstrate that this solution asymptotes to an excited state in past infinity in both cases. The result is interpreted in the light of the loss of unitarity for very small wavelengths. The outcome of such a nonunitary phase evolution should prepare each mode in the excited initial state that yields a finite twopoint function for all the parameter space. This will be constraining of the new physics that UV completes such scenarios.
Mon, 01 Jan 2018 00:00:00 GMT
https://www.repo.unihannover.de/handle/123456789/4929
20180101T00:00:00Z

Sustainability transitions and the spatial interface: Developing conceptual perspectives
https://www.repo.unihannover.de/handle/123456789/3884
Sustainability transitions and the spatial interface: Developing conceptual perspectives
LevinKeitel, Meike; Mölders, Tanja; Othengrafen, Frank; Ibendorf, Jens
Sustainability transitions research lacks a crucial perspective: the spatial dimension. The interrelations between space and sustainability transition processes are thus underexposed. The spatial dimension is, of course, implicitly addressed in transition research but it often remains unclear which spatial concept is used and how the spatial conditions are embedded in the transition processes. This paper approaches the problem in two steps: (1) analysing the various understandings of transitions research and their implications for different spatial concepts relating to spatial sustainability transition; and (2) focusing on different spatial concepts (from a positivist mode to relational and sociocultural approaches) and their reflections in different disciplines of social, natural and technical sciences as well as in practice. By identifying the links between sustainable transition approaches on the one hand and spatial conceptualizations on the other hand, this paper aims at deepening both the spatial perspective and the understanding of sustainable transition research. The results of this paper are three conceptual perspectives wherein space or spatial conceptualizations can provide added value for sustainability transition research in inter and transdisciplinary modes. These three perspectives include (1) space as a "bridging concept," (2) space as a "normative concept," and (3) space as an "approach to action.".
Mon, 01 Jan 2018 00:00:00 GMT
https://www.repo.unihannover.de/handle/123456789/3884
20180101T00:00:00Z