In our **Mathematical Physics and Field Theory Group**, we study the following subjects:

**1- Hamiltonian structure of systems with diffeomorphism symmetry**

Hilbert-Einstein gravity and the other gravity models that are built based on diffeomorphism symmetry also have reparametrization symmetry. Our experience about global symmetry in physics says that we can construct generators of symmetry groups in phase space and evaluate their algebra. This method is not enough clear about systems with reparametrization symmetry. There are efforts for construction of Hamiltonian structure for Hilbert–Einstein model and some other famous models, but still there is much work to do.

**2- Noether symmetry of systems with diffeomorphism symmetry in Lagrangian formulation**

Noether identity has a basic role in understanding of gauge symmetry theories. Gauge symmetry of systems with diffeomorphism symmetry is known by the transformation that corresponds to reparametrization symmetry. By evaluating Euler derivative and singularity of Hessian Matrix, we can achieve symmetries of a system in the Lagrangian formulation. Now, we are working on the Polyakov action and topological massive gravity (TMG) action, but there are some models that we can work on them in future.

**3- Boundary conditions as Dirac constraints**

In Lagrangian formulation, boundary conditions are acquired by variation of action. Second derivatives do not appear in these conditions. In Hamiltonian formulation, the boundary conditions are considered as identities that contain coordinate and momentum. The idea is that the boundary conditions are added to the system as Dirac constraints in Hamiltonian formulation. This idea is not old and in recent decade has some achievement like access to non-commutative space in string theory.

Related faculty:

- Mathematical Physics and Field Theory