Välkommen till en dubbel föreläsning i seminarieserien i matematik.
Föreläsare/Lecturer 1, 13.00-13.45
Fritiof Persson, doktorand, institutionen för matematik, Linnéuniversitetet
Born’s rule from second quantization
We view phase factors not only as redundancies in the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. We postulate that a quantum observable corresponds to unitary representations of an abelian group, the irreducible subrepresentations of which correspond to the observable's outcomes. It is shown that this identification agrees with the conventional identification as self-adjoint operators.
The upshot of this formalism is that we may 'second quantize' the representation to which an observable corresponds, thus obtaining the corresponding Fock space representation. This Fock space representation is then too identifiable as an observable in the same sense, the outcomes of which are naturally interpretable as ensembles of outcomes of the corresponding non-second quantized observable. We adopt the frequency interpretation of probability, i.e. as the average occurrence of the outcome in question, from which we deduce Born's rule by enforcing the notion 'average' to such that are invariant under contextual global phase factors of the second quantized initial state.
Föreläsare/Lecturer 2, 14.00-14.45
Ehsan Pourhadi, professor, Teherans universitet, Iran
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u.
Throughout this presentation, the basic properties of these graphs are obtained. The new concept is connected with symmetry conditions in graphs; moreover, some local operations on such graphs are studied. Some applications are involved.
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