Open AccessSymmetries in the projection evolution model
Author(s) -
P. ̧edrak Aleksandra,
A. Góźdź,
Marek Góźdź
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1416/1/012027
Subject(s) - homogeneous space , conservation law , formalism (music) , eigenvalues and eigenvectors , unitary state , casimir element , orthographic projection , casimir effect , mathematics , mathematical physics , projection (relational algebra) , pure mathematics , theoretical physics , physics , algebra over a field , classical mechanics , quantum mechanics , mathematical analysis , geometry , algorithm , law , art , musical , political science , cellular algebra , visual arts , algebra representation
Some introductory results concerning symmetries and conservation laws within the Projection Evolution (PEv) formalism are presented. It is shown that the PEv formalism conserves the quantum probability distributions after unitary transformations of the evolution operators represented by the orthogonal resolution of unity. Some conditions for transformations selecting the states with equal transition probabilities are found. A relation between a given symmetry represented by a Lie group and PEv conservation of the eigenvalues of the Casimir operator is derived.