Extended Lagrange and Hamilton Formalism for Point Mechanics and Covariant Hamilton Field Theory

10.1142/9034 ◽  
2022 ◽  
Author(s):  
Jürgen Struckmeier ◽  
Walter Greiner
Keyword(s):  
Field Theory ◽  
Hamilton Formalism

scholarly journals CANONICAL TENSOR MODELS WITH LOCAL TIME

2012 ◽  
Vol 27 (05) ◽  
pp. 1250020 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Local Time ◽  
String Field Theory ◽  
Dynamical Variable ◽  
Tensor Model ◽  
Canonical Variables ◽  
Hamilton Formalism ◽  
Tensor Models ◽  
Constraint Algebra

It is an intriguing question how local time can be introduced in the emergent picture of space–time. In this paper, this problem is discussed in the context of tensor models. To consistently incorporate local time into tensor models, a rank-three tensor model with first class constraints in Hamilton formalism is presented. In the limit of usual continuous spaces, the algebra of constraints reproduces that of general relativity in Hamilton formalism. While the momentum constraints can be realized rather easily by the symmetry of the tensor models, the form of the Hamiltonian constraints is strongly limited by the condition of the closure of the whole constraint algebra. Thus the Hamiltonian constraints have been determined on the assumption that they are local and at most cubic in canonical variables. The form of the Hamiltonian constraints has similarity with the Hamiltonian in the c < 1 string field theory, but it seems impossible to realize such a constraint algebras in the framework of vector or matrix models. Instead these models are rather useful as matter theories coupled with the tensor model. In this sense, a three-index tensor is the minimum-rank dynamical variable necessary to describe gravity in terms of tensor models.

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