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The formalism of quantum field theory in operator form, based on the anti self-adjoint operators of the imaginary coordinate and momentum and the self-adjoint operators of the real coordinate, momentum, energy and time, is used in…
The fractionalization of microscopic degrees of freedom is a remarkable manifestation of strong interactions in quantum many-body systems. Analytical studies of this phenomenon are primarily based on two distinct frameworks: field theories…
Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on…
We revisit a non-perturbation theory of quantum gravity in $1.5$ order underlying an emergent gravitational pair of $(4{\bar 4})$-brane with a renewed interest. In particular the formulation is governed by a geometric torsion ${\cal H}_3$…
We demonstrate in detail how the space of two-dimensional quantum field theories can be parametrized by off-shell states of a free closed string moving in a flat background. The dynamic equation corresponding to the condition of conformal…
We propose an analogue of spin fields for the relativistic RNS-particle in 4 dimensions, in order to describe Ramond-Ramond states as "two-particle" excitations on the world line. On a natural representation space we identify a differential…
The behavior of spin doublets is known to play a major role in nuclear structure and shell effects. Pseudo-spin doublets are also known to impact the single-particle spectrum. The covariant framework, having these two effects encoded in its…
Quantum entanglement reflects itself through non-local correlations among the subsystems of a quantum system. This thesis focuses on constructing a complete set of local invariants characterizing symmetric two qubit systems and analyzing…
Of great recent interest in condensed matter physics are phenomena of coexistence of quantum and classical properties in the same material. Such duality occurs in certain mixed-spin antiferromagnets composed of quantum spin chains…
It has been suggested that higher-derivative gravity theories coupled to a scalar field with shift symmetry may be an important candidate for a quantum gravity. We show that this class of gravity theories are renormalizable in D = 3 and 4…
The Fierz-Pauli (FP) free field theory for massive spin 2 particles can be extended, in a spacetime of (1+2) dimensions (3D), to a generally covariant parity-preserving interacting field theory, in at least two ways. One is "new massive…
The coupled cluster method (CCM) has previously been applied to study the ground- and excited-state properties of many different types of frustrated and unfrustrated quantum spin systems. A common feature in the application of the CCM is to…
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
A quantal guiding center theory allowing to systematically study the separation of the different time scale behaviours of a quantum charged spinning particle moving in an external inhomogeneous magnetic filed is presented. A suitable set of…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
We consider massive higher-spin multiplets coupled to quantum gravity and compute their contributions to the gravitational beta functions at one loop. Such theories, if quantized with the Feynman prescription, would contain ghosts. Instead,…
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…
We observe cavity mediated spin-dependent interactions in an off-resonantly driven multi-level atomic Bose-Einstein condensate that is strongly coupled to an optical cavity. Applying a driving field with adjustable polarization, we identify…
We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…