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Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…

A few recent innovations of applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly…

We study worldsheet conformal invariance for bosonic string propagating in a curved background using the hamiltonian formalism. In order to formulate the problem in a background independent manner we first rewrite the worldsheet theory in a…

Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space -- time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent,…

We present physical arguments based on loop space representations for Dirac/Klein gordon determinants that some suitable Fermionic String Ising models at the critical point and defined on the space-time base manifold are formal quantum…

Among the available quantum gravity proposals, string theory, loop quantum gravity, non-commutative geometry, group field theory, causal sets, asymptotic safety, causal dynamical triangulation, emergent gravity are among the best motivated…

We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…

Making use of the duality transformation, we derive in the Londons' limit of the Abelian Higgs Model string representation for the 't Hooft loop average defined on the string world-sheet, which yields the values of two coefficient functions…

By using the hybrid formalism, superstrings in four-dimensional NS-NS plane waves are studied in a manifest supersymmetric manner. This description of the superstring is obtained by a field redefinition of the RNS worldsheet fields and…

The structure of quantum interactions with fields of helicity two ("gravitons") is strongly constrained by three principles: positivity (Hilbert space), covariance, and locality of observables. To fulfil them simultaneously, some…

In this paper, we address the nature of spacetime in quantum gravity in light of a new version of the holographic principle that has established a relationship between string theory and polymer holonomy structures similar to Loop Quantum…

In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…

We clarify the nature of the graviton as a bound state in open-string field theory: The flat metric in the action appears as the vacuum value of an OPEN string field. The bound state appears as a composite field in the FREE field theory.

In the first part of this paper I review the construction of the realistic free fermionic models, as well as current attempts to study aspects of these models in the nonperturbative framework of M- and F-theories. I discuss the recent…

In a recent proposal we applied methods from constructive QFT to derive a Hamiltonian Renormalisation Group in order to employ it ultimately for canonical quantum gravity. The proposal was successfully tested for free scalar fields and thus…

We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism…

We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…

The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills…

As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism…

We review the approach to quantum gravity based on supersymmetry, strings, and holography. This includes a survey of black holes in higher-dimensions, supersymmetry and supergravity, as well as string theory, black hole microstates, and the…