MG11 |
Participant |
Tillman, Philip | |
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Institution |
University of Pittsburgh, Dept. of Physics and Astronomy - 3941 O'Hara St.; 225 Old Engineering Hall - Pittsburgh - PA - USA | |
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Session |
Talk |
Abstract |
|
S1 |
THE KLEIN-GORDON EQUATION AND QFT'S ON A CURVED SPACE-TIME: AN APPLICATION OF DEFORMATION QUANTIZATION |
The aim of the talk is to define and show how to apply deformation quantization to get the Klein-Gordon (KG) equation on a general manifold. In particular, we will use a generalization of the Moyal star-product called the Fedosov star-product. Using the Moyal star-product one can reproduce quantum mechanics on a Euclidean space that is invariant under all canonical transformations. The Fedosov star-product provides the same framework on a general manifold. The structures on the phase-space of our manifold used in the construction of the Fedosov star-product are the Poisson bracket, the phase-space connection, and the space-time metric. After the construction of the Fedosov star-product, a dynamical principle is introduced which becomes the KG equation. We outline the framework for a quantum field theory of a free spin 0 field in the case of dS/AdS. A summary of recent results for dS, AdS, and Schwarzschild space-times is given. |
|
QG2 |
THE KLEIN-GORDON EQUATION AND QFT'S ON A CURVED SPACE-TIME: AN APPLICATION OF DEFORMATION QUANTIZATION |
The aim of the talk is to define and show how to apply deformation quantization to get the Klein-Gordon (KG) equation on a general manifold. In particular, we will use a generalization of the Moyal star-product called the Fedosov star-product. Using the Moyal star-product one can reproduce quantum mechanics on a Euclidean space that is invariant under all canonical transformations. The Fedosov star-product provides the same framework on a general manifold. The structures on the phase-space of our manifold used in the construction of the Fedosov star-product are the Poisson bracket, the phase-space connection, and the space-time metric. After the construction of the Fedosov star-product, a dynamical principle is introduced which becomes the KG equation. We outline the framework for a quantum field theory of a free spin 0 field in the case of dS/AdS. A summary of recent results for dS, AdS, and Schwarzschild space-times is given. |
|
QG4 |
THE KLEIN-GORDON EQUATION AND QFT'S ON A CURVED SPACE-TIME: AN APPLICATION OF DEFORMATION QUANTIZATION |
The aim of the talk is to define and show how to apply deformation quantization to get the Klein-Gordon (KG) equation on a general manifold. In particular, we will use a generalization of the Moyal star-product called the Fedosov star-product. Using the Moyal star-product one can reproduce quantum mechanics on a Euclidean space that is invariant under all canonical transformations. The Fedosov star-product provides the same framework on a general manifold. The structures on the phase-space of our manifold used in the construction of the Fedosov star-product are the Poisson bracket, the phase-space connection, and the space-time metric. After the construction of the Fedosov star-product, a dynamical principle is introduced which becomes the KG equation. We outline the framework for a quantum field theory of a free spin 0 field in the case of dS/AdS. A summary of recent results for dS, AdS, and Schwarzschild space-times is given. |