Triangle Seminars
Wednesday, 20 Jan 2016
Gronewold-Moyal Mechanics: From quantum mechanics to higher spin gravity and matrix models
📍 London
Mauricio Valenzuela
(Chile Austral U., Valdivia)
Abstract:
The goal of this talk is to show some uses of the Gronewold-Moyal product in physics and new applications.
In the first part of this talk we review the approach of Gronewold and Moyal in the quantization of classical systems. Then we remark algebraic aspects related to the representation of symplectic algebras and extensions of Anti-de-Sitter algebras. Subsequently we describe how these aspects are used in higher spin gravity.
In the second part of this talk we present some new advances. We quantize a particular class of algebraic varieties, involving multivectors, and which contains Minkowski space slices. We show that these non-commutative geometries are solutions of known matrix models and some simple extensions of them. Then we present new models which describe the dynamics of extended objects in close resemblance to the equations of Hamiltonian systems. We also introduce statistical distributions in these spaces which encode their coordinates spectra.
The goal of this talk is to show some uses of the Gronewold-Moyal product in physics and new applications.
In the first part of this talk we review the approach of Gronewold and Moyal in the quantization of classical systems. Then we remark algebraic aspects related to the representation of symplectic algebras and extensions of Anti-de-Sitter algebras. Subsequently we describe how these aspects are used in higher spin gravity.
In the second part of this talk we present some new advances. We quantize a particular class of algebraic varieties, involving multivectors, and which contains Minkowski space slices. We show that these non-commutative geometries are solutions of known matrix models and some simple extensions of them. Then we present new models which describe the dynamics of extended objects in close resemblance to the equations of Hamiltonian systems. We also introduce statistical distributions in these spaces which encode their coordinates spectra.
Posted by: KCL
Polygon Seminar: SUSY field theories and matrix models
Nadav Drukker
(KCL)
Abstract:
Matrix models are toy models for quantum field theories. They can be extremely complicated but can also be solved in a variety of ways. In my talk I will discuss general properties of matrix models and their solutions and focus on particular matrix models that arise in the study of 4d SUSY field theories. Those matrix models describe the index of the field theory, counting the number of states of the theory (with + sign for a boson and - for a fermion) and have been known for over 10 years. Though they look very complicated I will show how some simple tricks allow in certain cases to solve those matrix models exactly in terms of elementary functions. My talk will focus on the matrix model calculation and no specialized knowledge of SUSY field theories or indices would be required to follow it.
Matrix models are toy models for quantum field theories. They can be extremely complicated but can also be solved in a variety of ways. In my talk I will discuss general properties of matrix models and their solutions and focus on particular matrix models that arise in the study of 4d SUSY field theories. Those matrix models describe the index of the field theory, counting the number of states of the theory (with + sign for a boson and - for a fermion) and have been known for over 10 years. Though they look very complicated I will show how some simple tricks allow in certain cases to solve those matrix models exactly in terms of elementary functions. My talk will focus on the matrix model calculation and no specialized knowledge of SUSY field theories or indices would be required to follow it.
Posted by: IC