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This volume presents modern trends in the area of symmetries and
their applications based on contributions to the workshop "Lie
Theory and Its Applications in Physics" held near Varna (Bulgaria)
in June 2019. Traditionally, Lie theory is a tool to build
mathematical models for physical systems. Recently, the trend is
towards geometrization of the mathematical description of physical
systems and objects. A geometric approach to a system yields in
general some notion of symmetry, which is very helpful in
understanding its structure. Geometrization and symmetries are
meant in their widest sense, i.e., representation theory, algebraic
geometry, number theory, infinite-dimensional Lie algebras and
groups, superalgebras and supergroups, groups and quantum groups,
noncommutative geometry, symmetries of linear and nonlinear partial
differential operators, special functions, and others. Furthermore,
the necessary tools from functional analysis are included. This is
a large interdisciplinary and interrelated field. The topics
covered in this volume from the workshop represent the most modern
trends in the field : Representation Theory, Symmetries in String
Theories, Symmetries in Gravity Theories, Supergravity, Conformal
Field Theory, Integrable Systems, Polylogarithms, and
Supersymmetry. They also include Supersymmetric Calogero-type
models, Quantum Groups, Deformations, Quantum Computing and Deep
Learning, Entanglement, Applications to Quantum Theory, and
Exceptional Quantum Algebra for the standard model of particle
physics This book is suitable for a broad audience of
mathematicians, mathematical physicists, and theoretical
physicists, including researchers and graduate students interested
in Lie Theory.
This book is the second volume of the proceedings of the joint
conference X. International Symposium "Quantum Theory and
Symmetries" (QTS-X) and XII. International Workshop "Lie Theory and
Its Applications in Physics" (LT-XII), 19-25 June 2017, Varna,
Bulgaria. The QTS series started around the core concept that
symmetries underlie all descriptions of quantum systems. It has
since evolved into a symposium on the frontiers of theoretical and
mathematical physics. The LT series covers the whole field of Lie
Theory in its widest sense together with its applications in many
facets of physics. As an interface between mathematics and physics
the workshop serves as a meeting place for mathematicians and
theoretical and mathematical physicists. In the division of the
material between the two volumes, the Editor has tried to select
for the first and second volumes papers that are more oriented
toward mathematics and physics, respectively. However, this
division is relative since many papers could have been placed in
either volume. The topics covered in this volume represent the most
modern trends in the fields of the joint conferences: symmetries in
string theories, conformal field theory, holography, gravity
theories and cosmology, gauge theories, foundations of quantum
theory, nonrelativistic and classical theories.
This book is the first volume of proceedings from the joint
conference X International Symposium "Quantum Theory and
Symmetries" (QTS-X) and XII International Workshop "Lie Theory and
Its Applications in Physics" (LT-XII), held on 19-25 June 2017 in
Varna, Bulgaria. The QTS series was founded on the core principle
that symmetries underlie all descriptions of quantum systems. It
has since evolved into a symposium at the forefront of theoretical
and mathematical physics. The LT series covers the whole field of
Lie theory in its widest sense, together with its applications in
many areas of physics. As an interface between mathematics and
physics, the workshop serves as a meeting place for mathematicians
and theoretical and mathematical physicists. In dividing the
material between the two volumes, the Editor has sought to select
papers that are more oriented toward mathematics for the first
volume, and those focusing more on physics for the second. However,
this division is relative, since many papers are equally suitable
for either volume. The topics addressed in this volume represent
the latest trends in the fields covered by the joint conferences:
representation theory, integrability, entanglement, quantum groups,
number theory, conformal geometry, quantum affine superalgebras,
noncommutative geometry. Further, they present various mathematical
results: on minuscule modules, symmetry breaking operators,
Kashiwara crystals, meta-conformal invariance, the superintegrable
Zernike system.
This book is the second volume of the proceedings of the joint
conference X. International Symposium "Quantum Theory and
Symmetries" (QTS-X) and XII. International Workshop "Lie Theory and
Its Applications in Physics" (LT-XII), 19-25 June 2017, Varna,
Bulgaria. The QTS series started around the core concept that
symmetries underlie all descriptions of quantum systems. It has
since evolved into a symposium on the frontiers of theoretical and
mathematical physics. The LT series covers the whole field of Lie
Theory in its widest sense together with its applications in many
facets of physics. As an interface between mathematics and physics
the workshop serves as a meeting place for mathematicians and
theoretical and mathematical physicists. In the division of the
material between the two volumes, the Editor has tried to select
for the first and second volumes papers that are more oriented
toward mathematics and physics, respectively. However, this
division is relative since many papers could have been placed in
either volume. The topics covered in this volume represent the most
modern trends in the fields of the joint conferences: symmetries in
string theories, conformal field theory, holography, gravity
theories and cosmology, gauge theories, foundations of quantum
theory, nonrelativistic and classical theories.
This volume presents modern trends in the area of symmetries and
their applications based on contributions from the workshop "Lie
Theory and Its Applications in Physics", held near Varna, Bulgaria,
in June 2015. Traditionally, Lie theory is a tool to build
mathematical models for physical systems.Recently, the trend has
been towards geometrization of the mathematical description of
physical systems and objects. A geometric approach to a system
yields in general some notion of symmetry, which is very helpful in
understanding its structure. Geometrization and symmetries are
employed in their widest sense, embracing representation theory,
algebraic geometry, number theory, infinite-dimensional Lie
algebras and groups, superalgebras and supergroups, groups and
quantum groups, noncommutative geometry, symmetries of linear and
nonlinear partial differential operators (PDO), special functions,
and others. Furthermore, the necessary tools from functional
analysis are included.
This volume presents modern trends in the area of symmetries and
their applications based on contributions from the workshop "Lie
Theory and Its Applications in Physics", held near Varna, Bulgaria,
in June 2015. Traditionally, Lie theory is a tool to build
mathematical models for physical systems.Recently, the trend has
been towards geometrization of the mathematical description of
physical systems and objects. A geometric approach to a system
yields in general some notion of symmetry, which is very helpful in
understanding its structure. Geometrization and symmetries are
employed in their widest sense, embracing representation theory,
algebraic geometry, number theory, infinite-dimensional Lie
algebras and groups, superalgebras and supergroups, groups and
quantum groups, noncommutative geometry, symmetries of linear and
nonlinear partial differential operators (PDO), special functions,
and others. Furthermore, the necessary tools from functional
analysis are included.
Traditionally, Lie theory is a tool to build mathematical models
for physical systems. Recently, the trend is towards geometrization
of the mathematical description of physical systems and objects. A
geometric approach to a system yields in general some notion of
symmetry which is very helpful in understanding its structure.
Geometrization and symmetries are meant in their widest sense,
i.e., representation theory, algebraic geometry,
infinite-dimensional Lie algebras and groups, superalgebras and
supergroups, groups and quantum groups, noncommutative geometry,
symmetries of linear and nonlinear PDE, special functions, and
others. Furthermore, the necessary tools from functional analysis
and number theory are included. This is a big interdisciplinary and
interrelated field. Samples of these fresh trends are presented in
this volume, based on contributions from the Workshop "Lie Theory
and Its Applications in Physics" held near Varna (Bulgaria) in June
2013. This book is suitable for a broad audience of mathematicians,
mathematical physicists, and theoretical physicists and researchers
in the field of Lie Theory.
Traditionally, Lie Theory is a tool to build mathematical models
for physical systems. Recently, the trend is towards geometrisation
of the mathematical description of physical systems and objects. A
geometric approach to a system yields in general some notion of
symmetry which is very helpful in understanding its structure.
Geometrisation and symmetries are meant in their broadest sense,
i.e., classical geometry, differential geometry, groups and quantum
groups, infinite-dimensional (super-)algebras, and their
representations. Furthermore, we include the necessary tools from
functional analysis and number theory. This is a large
interdisciplinary and interrelated field. Samples of these new
trends are presented in this volume, based on contributions from
the Workshop "Lie Theory and Its Applications in Physics" held near
Varna, Bulgaria, in June 2011. This book is suitable for an
extensive audience of mathematicians, mathematical physicists,
theoretical physicists, and researchers in the field of Lie Theory.
Traditionally, Lie theory is a tool to build mathematical models
for physical systems. Recently, the trend is towards geometrization
of the mathematical description of physical systems and objects. A
geometric approach to a system yields in general some notion of
symmetry which is very helpful in understanding its structure.
Geometrization and symmetries are meant in their widest sense,
i.e., representation theory, algebraic geometry,
infinite-dimensional Lie algebras and groups, superalgebras and
supergroups, groups and quantum groups, noncommutative geometry,
symmetries of linear and nonlinear PDE, special functions, and
others. Furthermore, the necessary tools from functional analysis
and number theory are included. This is a big interdisciplinary and
interrelated field. Samples of these fresh trends are presented in
this volume, based on contributions from the Workshop "Lie Theory
and Its Applications in Physics" held near Varna (Bulgaria) in June
2013. This book is suitable for a broad audience of mathematicians,
mathematical physicists, and theoretical physicists and researchers
in the field of Lie Theory.
Traditionally, Lie Theory is a tool to build mathematical models
for physical systems. Recently, the trend is towards geometrisation
of the mathematical description of physical systems and objects. A
geometric approach to a system yields in general some notion of
symmetry which is very helpful in understanding its structure.
Geometrisation and symmetries are meant in their broadest sense,
i.e., classical geometry, differential geometry, groups and quantum
groups, infinite-dimensional (super-)algebras, and their
representations. Furthermore, we include the necessary tools from
functional analysis and number theory. This is a large
interdisciplinary and interrelated field.
Samples of these new trends are presented in this volume, based on
contributions from the Workshop Lie Theory and Its Applications in
Physics held near Varna, Bulgaria, in June 2011.
This book is suitable for an extensive audience of mathematicians,
mathematical physicists, theoretical physicists, and researchers in
the field of Lie Theory."
This volume presents modern trends in the area of symmetries and
their applications based on contributions to the Workshop "Lie
Theory and Its Applications in Physics" held in Sofia, Bulgaria
(on-line) in June 2021. Traditionally, Lie theory is a tool to
build mathematical models for physical systems. Recently, the trend
is towards geometrization of the mathematical description of
physical systems and objects. A geometric approach to a system
yields in general some notion of symmetry which is very helpful in
understanding its structure. Geometrization and symmetries are
meant in their widest sense, i.e., representation theory, algebraic
geometry, number theory, infinite-dimensional Lie algebras and
groups, superalgebras and supergroups, groups and quantum groups,
noncommutative geometry, symmetries of linear and nonlinear partial
differential operators, special functions, and others. Furthermore,
the necessary tools from functional analysis are included. This is
a big interdisciplinary and interrelated field. The topics covered
in this Volume are the most modern trends in the field of the
Workshop: Representation Theory, Symmetries in String Theories,
Symmetries in Gravity Theories, Supergravity, Conformal Field
Theory, Integrable Systems, Quantum Computing and Deep Learning,
Entanglement, Applications to Quantum Theory, Exceptional quantum
algebra for the standard model of particle physics, Gauge Theories
and Applications, Structures on Lie Groups and Lie Algebras. This
book is suitable for a broad audience of mathematicians,
mathematical physicists, and theoretical physicists, including
researchers and graduate students interested in Lie Theory.
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