Related papers: Geometric flavours of Quantum Field theory on a Ca…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
This thesis explores Quantum Field Theory (QFT) on curved spacetimes using a geometric Hamiltonian approach to the Schr\"odinger-like representation. In particular it studies the theory of the scalar field described through its…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…
Rules of quantization and equations of motion for a finite-dimensional formulation of Quantum Field Theory are proposed which fulfill the following properties: a) both the rules of quantization and the equations of motion are covariant; b)…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…
The 2023 second edition of a 2006 encyclopedia article on mathematical aspects of quantum field theory in curved spacetimes (QFTCST). Section-titles (with new sections indicated with stars) are: Introduction and preliminaries, Construction…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…
We give a mathematical definition of dynamical evolution in quantum field theory, including evolution on space-like surfaces, and show its relationship with the axiomatic and perturbative approaches to QFT.
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
We consider the problem of evolving a quantum field between any two (in general, curved) Cauchy surfaces. Classically, this dynamical evolution is represented by a canonical transformation on the phase space for the field theory. We show…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
In our model of quantum gravity the quantum development of a Cauchy hypersurface is governed by a wave equation derived as the result of a canonical quantization process. To find physically interesting solutions of the wave equation we…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…