The specific transformative steps that occur from the multipotent through the mature cardiomyocyte state are determined in large part by changes in gene expression. The exact differentiation and developmental programs are tightly regulated in a step-wise systematic fashion based on the influence of specific instigating and signaling factors. Crucial to the observed cell behavior and tissue specific phenotypic differences are alterations in the organization, translocation and expression of nuclear proteins during differentiation. The cardiomyogenic differentiation of Mesenchymal Stem Cells (MSCs) remains a precarious process. Transplanted MSCs must respond to endogenous signaling molecules involved in early embryonic cardiomyogenesis by activating the specific gene regulatory network required for successful cardiomyogenesis and transdifferentiation. To do that, transplanted MSCs would have to be genuinely reprogrammed genetically to become functional cardiac myocytes. A consideration of recent experimental findings suggests that Bone morphogenic protein (BMP-2/4), insulin-like growth factor (IGF-1) and fibroblast growth factor (FGF-2) in combination is a potent inducer of MSC cardiomyogenesis. The development of an optimum and reliable in vitro culture milieu for directing their cardiomyogenesis will provide an indispensable model system for molecular studies and genetic manipulation.

Abstract:
In this paper we will study non-anticommutative perturbative quantum gravity on spacetime with a complex metric. After analysing the BRST symmetry of this non-anticommutative perturbative quantum gravity, we will also analyse the effect of shifting all the fields. We will construct a Lagrangian density which is invariant under the original BRST transformations and the shift transformations in the Batalin-Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this shift symmetry invariant Lagrangian density can be elegantly written down in superspace with a single Grassmann parameter.

Abstract:
In this paper we will study perturbative quantum gravity on supermanifolds with both noncommutative and non-anticommutative coordinates. We shall first analyses the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin-Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with two Grassmann parameters.

Abstract:
In this paper we shall consistently third quantize modified gravity. Then we shall analyse certain aspects of virtual black holes in this third quantized modified gravity. We will see how a statistical mechanical origin for the Bekenstein-Hawking entropy naturally arises in this model. Furthermore, in this model the area and thus the entropy of a real macroscopic black hole is quantized. Virtual black holes cause loss of quantum coherence and this gives an intrinsic entropy to all physical systems which can be used to define a direction of time and hence provide a solution to the problem of time.

Abstract:
In this paper we will study the spontaneous breakdown of the Lorentz symmetry by ghost condensation in perturbative quantum gravity. Our analysis will be done in the Curci-Ferrari gauge. We will also analyse modification of the BRST and the anti-BRST transformations by the formation of this ghost condensate. It will be shown that even though the modified BRST and the modified anti-BRST transformations are not nilpotent, their nilpotency is restored on-shell.

Abstract:
We discuss the BRST and anti-BRST symmetries for perturbative quantum gravity in noncommutative spacetime. In this noncommutative perturbative quantum gravity the sum of the classical Lagrangian density with a gauge fixing term and a ghost term is shown to be invariant the noncommutative BRST and the noncommutative anti-BRST transformations. We analyse the gauge fixing term and the ghost term in both linear as well as non-linear gauges. We also discuss the unitarity evolution of the theory and analyse the violation of unitarity of by introduction of a bare mass term in the noncommutative BRST and the noncommutative anti-BRST transformations.

Abstract:
This thesis consists of three parts. In the first part we review the quantization of Yang-Mills theories and perturbative quantum gravity in curved spacetime. In the second part we calculate the Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge. In the third part we investigate the physical equivalence of covariant Wightman graviton two-point function with the physical graviton two-point function. The Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, that if we regularize these divergences by introducing a finite mass and take the zero mass limit at the end, then the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. We thus find effective Feynman propagators for ghosts in Yang-Mills theories and perturbative quantum gravity by subtracting out these divergent modes. It is known that the covariant graviton two-point function in de Sitter spacetime is infrared divergent for some choices of gauge parameters. On the other hand it is also known that there are no infrared problems for the physical graviton two-point function obtained by fixing all gauge degrees of freedom, in global coordinates. We show that the covariant Wightman graviton two-point function is equivalent to the physical one in the sense that they result in the same two-point function of any local gauge-invariant quantity. Thus any infrared divergence in the Wightman graviton two-point function in de Sitter spacetime can only be an gauge artefact.

Abstract:
In this paper we will analyse the creation of the multiverse. We will first calculate the wave function for the multiverse using third quantization. Then we will fourth quantize this theory. We will show that there is no single vacuum state for this theory. Thus, we can end up with a multiverse, even after starting from a vacuum state. This will be used as a possible explanation for the creation of the multiverse. We also analyse the effect of interactions in this fourth quantized theory.

Abstract:
In this paper we will analyse the third quantization of a model of super-group field cosmology with gauge symmetry. The effect of creation and annihilation of bosonic and fermionic universes in the multiverse will also be analysed. We will also construct a third quantized Noether's charge which will be conserved even when the number of universes is not conserved. Finally, we will construct both the third quantized BRST and the third quantized anti-BRST charges for this theory and use them to show that the creation and annihilation of universes is a unitarity process.