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This book presents a selection of Prof. Matteo Campanella's
writings on the interpretative aspects of quantum mechanics and on
a possible derivation of Born's rule - one of the key principles of
the probabilistic interpretation of quantum mechanics - that is
independent of any priori probabilistic interpretation. This topic
is of fundamental interest, and as such is currently an active area
of research. Starting from a natural method of defining such a
state, Campanella found that it can be characterized through a
partial density operator, which occurs as a consequence of the
formalism and of a number of reasonable assumptions connected with
the notion of a state. The book demonstrates that the density
operator arises as an orbit invariant that has to be interpreted as
probabilistic, and that its quantitative implementation is
equivalent to Born's rule. The appendices present various
mathematical details, which would have interrupted the continuity
of the discussion if they had been included in the main text. For
instance, they discuss baricentric coordinates, mapping between
Hilbert spaces, tensor products between linear spaces, orbits of
vectors of a linear space under the action of its structure group,
and the class of Hilbert space as a category.
This book presents a selection of Prof. Matteo Campanella's
writings on the interpretative aspects of quantum mechanics and on
a possible derivation of Born's rule - one of the key principles of
the probabilistic interpretation of quantum mechanics - that is
independent of any priori probabilistic interpretation. This topic
is of fundamental interest, and as such is currently an active area
of research. Starting from a natural method of defining such a
state, Campanella found that it can be characterized through a
partial density operator, which occurs as a consequence of the
formalism and of a number of reasonable assumptions connected with
the notion of a state. The book demonstrates that the density
operator arises as an orbit invariant that has to be interpreted as
probabilistic, and that its quantitative implementation is
equivalent to Born's rule. The appendices present various
mathematical details, which would have interrupted the continuity
of the discussion if they had been included in the main text. For
instance, they discuss baricentric coordinates, mapping between
Hilbert spaces, tensor products between linear spaces, orbits of
vectors of a linear space under the action of its structure group,
and the class of Hilbert space as a category.
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