A generalized form of the Raychaudhuri equation

In this work, we have attempted to generalize the Raychaudhuri equation by using the concept of foliation of spacetime. Some studies are performed with a few special cases and their physical implication are discussed.

Vacuum polarization of generalized quantum electrodynamics in the Heisenberg picture

In this work, we consider the generalized quantum electrodynamics proposed by Podolsky in Heisenberg picture via Källén methodology. We investigate the effects of higher-order derivatives to understand the qualitative and quantitative aspects of vacuum polarization. In addition, the most general structure of induced current and polarization tensor that emerge naturally by a perturbative scheme “à la” Källén is also obtained. Afterward, we discuss the physical implication of charge renormalization in the perspective of unitary and stable Podolsky theory.

The null identities for boundary operators in the (2, 2p + 1) minimal gravity

By using the matrix model representation, we show that correlation numbers of boundary-changing operators (BCOs) in $(2,2p+1)$ minimal Liouville gravity satisfy some identities, which we call the null identities. These identities enable us to express the correlation numbers of BCOs in terms of those of boundary-preserving operators. We also discuss a physical implication of the null identities as the manifestation of the boundary interaction.