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This book focuses on a critical discussion of the status and
prospects of current approaches in quantum mechanics and quantum
field theory, in particular concerning gravity. It contains a
carefully selected cross-section of lectures and discussions at the
seventh conference "Progress and Visions in Quantum Theory in View
of Gravity" which took place in fall 2018 at the Max Planck
Institute for Mathematics in the Sciences in Leipzig. In contrast
to usual proceeding volumes, instead of reporting on the most
recent technical results, contributors were asked to discuss
visions and new ideas in foundational physics, in particular
concerning foundations of quantum field theory. A special focus has
been put on the question of which physical principles of quantum
(field) theory can be considered fundamental in view of gravity.
The book is mainly addressed to mathematicians and physicists who
are interested in fundamental questions of mathematical physics. It
allows the reader to obtain a broad and up-to-date overview of a
fascinating active research area.
This book focuses on a critical discussion of the status and
prospects of current approaches in quantum mechanics and quantum
field theory, in particular concerning gravity. It contains a
carefully selected cross-section of lectures and discussions at the
seventh conference "Progress and Visions in Quantum Theory in View
of Gravity" which took place in fall 2018 at the Max Planck
Institute for Mathematics in the Sciences in Leipzig. In contrast
to usual proceeding volumes, instead of reporting on the most
recent technical results, contributors were asked to discuss
visions and new ideas in foundational physics, in particular
concerning foundations of quantum field theory. A special focus has
been put on the question of which physical principles of quantum
(field) theory can be considered fundamental in view of gravity.
The book is mainly addressed to mathematicians and physicists who
are interested in fundamental questions of mathematical physics. It
allows the reader to obtain a broad and up-to-date overview of a
fascinating active research area.
This monograph introduces the basic concepts of the theory of
causal fermion systems, a recent approach to the description of
fundamental physics. The theory yields quantum mechanics, general
relativity and quantum field theory as limiting cases and is
therefore a candidate for a unified physical theory. From the
mathematical perspective, causal fermion systems provide a general
framework for describing and analyzing non-smooth geometries and
"quantum geometries". The dynamics is described by a novel
variational principle, called the causal action principle. In
addition to the basics, the book provides all the necessary
mathematical background and explains how the causal action
principle gives rise to the interactions of the standard model plus
gravity on the level of second-quantized fermionic fields coupled
to classical bosonic fields. The focus is on getting a
mathematically sound connection between causal fermion systems and
physical systems in Minkowski space. The book is intended for
graduate students entering the field, and is furthermore a valuable
reference work for researchers in quantum field theory and quantum
gravity.
Quantum physics has been highly successful for more than 90 years.
Nevertheless, a rigorous construction of interacting quantum field
theory is still missing. Moreover, it is still unclear how to
combine quantum physics and general relativity in a unified
physical theory. Attacking these challenging problems of
contemporary physics requires highly advanced mathematical methods
as well as radically new physical concepts. This book presents
different physical ideas and mathematical approaches in this
direction. It contains a carefully selected cross-section of
lectures which took place in autumn 2014 at the sixth conference
``Quantum Mathematical Physics - A Bridge between Mathematics and
Physics'' in Regensburg, Germany. In the tradition of the other
proceedings covering this series of conferences, a special feature
of this book is the exposition of a wide variety of approaches,
with the intention to facilitate a comparison. The book is mainly
addressed to mathematicians and physicists who are interested in
fundamental questions of mathematical physics. It allows the reader
to obtain a broad and up-to-date overview of a fascinating active
research area.
This monograph introduces the basic concepts of the theory of
causal fermion systems, a recent approach to the description of
fundamental physics. The theory yields quantum mechanics, general
relativity and quantum field theory as limiting cases and is
therefore a candidate for a unified physical theory. From the
mathematical perspective, causal fermion systems provide a general
framework for describing and analyzing non-smooth geometries and
"quantum geometries". The dynamics is described by a novel
variational principle, called the causal action principle. In
addition to the basics, the book provides all the necessary
mathematical background and explains how the causal action
principle gives rise to the interactions of the standard model plus
gravity on the level of second-quantized fermionic fields coupled
to classical bosonic fields. The focus is on getting a
mathematically sound connection between causal fermion systems and
physical systems in Minkowski space. The book is intended for
graduate students entering the field, and is furthermore a valuable
reference work for researchers in quantum field theory and quantum
gravity.
Quantum physics has been highly successful for more than 90 years.
Nevertheless, a rigorous construction of interacting quantum field
theory is still missing. Moreover, it is still unclear how to
combine quantum physics and general relativity in a unified
physical theory. Attacking these challenging problems of
contemporary physics requires highly advanced mathematical methods
as well as radically new physical concepts. This book presents
different physical ideas and mathematical approaches in this
direction. It contains a carefully selected cross-section of
lectures which took place in autumn 2014 at the sixth conference
``Quantum Mathematical Physics - A Bridge between Mathematics and
Physics'' in Regensburg, Germany. In the tradition of the other
proceedings covering this series of conferences, a special feature
of this book is the exposition of a wide variety of approaches,
with the intention to facilitate a comparison. The book is mainly
addressed to mathematicians and physicists who are interested in
fundamental questions of mathematical physics. It allows the reader
to obtain a broad and up-to-date overview of a fascinating active
research area.
One of the most challenging problems of contemporary theoretical
physics is the mathematically rigorous construction of a theory
which describes gravitation and the other fundamental physical
interactions within a common framework. The physical ideas which
grew from attempts to develop such a theory require highly advanced
mathematical methods and radically new physical concepts. This book
presents different approaches to a rigorous unified description of
quantum fields and gravity. It contains a carefully selected
cross-section of lively discussions which took place in autumn 2010
at the fifth conference "Quantum field theory and gravity -
Conceptual and mathematical advances in the search for a unified
framework" in Regensburg, Germany. In the tradition of the other
proceedings covering this series of conferences, a special feature
of this book is the exposition of a wide variety of approaches,
with the intention to facilitate a comparison. The book is mainly
addressed to mathematicians and physicists who are interested in
fundamental questions of mathematical physics. It allows the reader
to obtain a broad and up-to-date overview of a fascinating active
research area.
One of the most challenging problems of contemporary theoretical
physics is the mathematically rigorous construction of a theory
which describes gravitation and the other fundamental physical
interactions within a common framework. The physical ideas which
grew from attempts to develop such a theory require highly advanced
mathematical methods and radically new physical concepts. This book
presents different approaches to a rigorous unified description of
quantum fields and gravity. It contains a carefully selected
cross-section of lively discussions which took place in autumn 2010
at the fifth conference "Quantum field theory and gravity -
Conceptual and mathematical advances in the search for a unified
framework" in Regensburg, Germany. In the tradition of the other
proceedings covering this series of conferences, a special feature
of this book is the exposition of a wide variety of approaches,
with the intention to facilitate a comparison. The book is mainly
addressed to mathematicians and physicists who are interested in
fundamental questions of mathematical physics. It allows the reader
to obtain a broad and up-to-date overview of a fascinating active
research area.
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