Related papers: Geometric formulation of the Covariant Phase Space…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint…
The present thesis aims at providing a unified description of radiative phase spaces in General Relativity for any value of the cosmological constant using covariant phase space methods. We start by considering generic asymptotically…
We prove a closed formula for leading Gopakumar- Vafa BPS invariants of local Calabi-Yau geometries given by the canonical line bundles of toric Fano surfaces. It shares some similar features with Goettsche-Yau-Zaslow formula: Connection…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) in semi-infinite space-time. In non-relativistic limit ($x\rightarrow\epsilon x, t\rightarrow t, \epsilon\rightarrow 0$), boundary conformal algebra changes…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
It has long been established that certain higher-dimensional topological phases of matter support extended objects like quasi-strings and quasi-membranes in their bulk states. In this study, we investigate the physics of these topological…
We describe the volume dependence of matrix elements of local boundary fields to all orders in inverse powers of the volume. Using the scaling boundary Lee-Yang model as testing ground, we compare the matrix elements extracted from boundary…
We present a robust method to find region-level correspondences between shapes, which are invariant to changes in geometry and applicable across multiple shape representations. We generate simplified shape graphs by jointly decomposing the…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
Covariant phase space quantization attempts to quantize the full space of classical solutions, leading to a quantum theory in which the usual time coordinate is missing. In this paper we explore how the time evolution of the quantum states…
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…
Many physically important mechanical systems may be described with a Lie group $G$ as configuration space. According to the well-known Noether's theorem, underlying symmetries of the Lie group may be used to considerably reduce the…
A typical geometry extracted from the path integral of a quantum theory of gravity might be quite complicated in the UV region. Even if such a configuration is not physical, it may be of interest to understand the details of its nature,…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
We motivate and survey the theory of BPS invariants of categories and BPS cohomology of stacks, indicating applications in enumerative geometry and representation theory, as well as recent advances.
In this paper I give overviews of the polysymplectic approach to covariant Hamiltonian field theory and the simplest geometric quantization of classical particle theories. I then give a synopsis of a recently proposed toy model for applying…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in…
We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new…