Classification of constraints using chain by chain method

We introduce "chain by chain" method for constructing the constraint structure of a system possessing both first and second class constraints. We show that the whole constraints can be classified into completely irreducible first or second class chains. We found appropriate redefinition of second class constraints to obtain a symplectic algebra among them.Comment: 23 pages, to appear in Int. J. Mod. Phys.

Constraint structure in modified Faddeev-Jackiw method

We show that in modified Faddeev-Jackiw formalism, first and second class constraints appear at each level, and the whole constraint structure is in exact correspondence with level by level method of Dirac formalism.Comment: 11 pages, No figure

Casimir-like corrections to the classical tensions of the strings and membranes

We find the Casimir-like energies for strings and membranes. We show that the related Casimir forces can be interpreted as quantum corrections to the classical tensions of the strings and membranes. We see that these corrections always increase the tensions of the circular string as well as spherical membrane, while for the straight string, rectangular and cylindrical membranes, these Casimir forces may increase or decrease the tensions. So we find that the quantum vacuum can break the (tensional) isotropy of the rectangular and cylindrical membranes. Also obtaining the nonzero-temperature Casimir energy, we find relations for the tensions at nonzero temperature.Comment: 14 pages, 2 figures; v8: the version accepted in PTE

Holographic Subregion Complexity for Singular Surfaces

Recently holographic prescriptions are proposed to compute quantum complexity of a given state in the boundary theory. A specific proposal known as `holographic subregion complexity' is supposed to calculate the the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cutoff, due to the singularities of a family of surfaces including a kink in (2+1)-dimension and cones in even dimensional field theories. We find examples of new divergent terms such as square logarithm and negative powers times the logarithm of the UV cut-off parameter.Comment: 30 page

On the classification of consistent boundary conditions for f(R) \mathit{f}(\mathit{R})-Gravity

Using a completely covariant approach, we discuss the role of boundary conditions (BCs) and the corresponding Gibbons--Hawking--York (GHY) terms in $\mathit{f}(\mathit{R})$-gravity in arbitrary dimensions. We show that $f(\mathit{R})$-gravity, as a higher derivative theory, is not described by a degenerate Lagrangian, in its original form. Hence, without introducing additional variables, one can not obtain consistent BCs, even by adding the GHY terms (except for $f(\mathit{R})=R$). However, following the Ostrogradsky approach, we can introduce a scalar field in the framework of Brans-Dicke formalism to the system to have consistent BCs by considering appropriate GHY terms. In addition to the Dirichlet BC, the GHY terms for both Neumann and two types of mixed BCs are derived. We show the remarkable result that the $f(\mathit{R})$-gravity is itself compatible with one type of mixed BCs, in $D$ dimension, i.e. it doesn't require any GHY term. For each BC, we rewrite the GHY term in terms of Arnowit-Deser-Misner (ADM) variables.Comment: 21 page