About: Toda field theory

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In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Kac–Moody algebra and a specific Lagrangian. Fixing the Kac–Moody algebra to have rank , that is, the Cartan subalgebra of the algebra has dimension , the Lagrangian can be written The background spacetime is 2-dimensional Minkowski space, with space-like coordinate and timelike coordinate . Greek indices indicate spacetime coordinates. The inner product is the restriction of the Killing form to the Cartan subalgebra.

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  • In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Kac–Moody algebra and a specific Lagrangian. Fixing the Kac–Moody algebra to have rank , that is, the Cartan subalgebra of the algebra has dimension , the Lagrangian can be written The background spacetime is 2-dimensional Minkowski space, with space-like coordinate and timelike coordinate . Greek indices indicate spacetime coordinates. For some choice of root basis, is the th simple root. This provides a basis for the Cartan subalgebra, allowing it to be identified with . Then the field content is a collection of scalar fields , which are scalar in the sense that they transform trivially under Lorentz transformations of the underlying spacetime. The inner product is the restriction of the Killing form to the Cartan subalgebra. The are integer constants, known as Kac labels or Dynkin labels. The physical constants are the mass and the coupling constant . (en)
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  • In mathematics and physics, specifically the study of field theory and partial differential equations, a Toda field theory, named after Morikazu Toda, is specified by a choice of Kac–Moody algebra and a specific Lagrangian. Fixing the Kac–Moody algebra to have rank , that is, the Cartan subalgebra of the algebra has dimension , the Lagrangian can be written The background spacetime is 2-dimensional Minkowski space, with space-like coordinate and timelike coordinate . Greek indices indicate spacetime coordinates. The inner product is the restriction of the Killing form to the Cartan subalgebra. (en)
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  • Toda field theory (en)
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