Related papers: Canonical SO(2,4)-invariant quantization in confor…
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…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
We formulate conformal field theory in the setting of algebraic quantum field theory as Haag-Kastler nets of local observable algebras with diffeomorphism covariance on the two-dimensional Minkowski space. We then obtain a decomposition of…
We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum…
We present a simple, systematic and practical method to construct conformally invariant equations in arbitrary Riemann spaces. This method that we call "Weyl-to-Riemann" is based on two features of Weyl geometry. i) A Weyl space is defined…
A simple model for the localization of the category $\mathbf{CLoc}_2$ of oriented and time-oriented globally hyperbolic conformal Lorentzian $2$-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of…
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…
A covariant scalar representation of $iosp(d,2/2)$ is constructed and analysed in comparison with existing methods for the quantization of the scalar relativistic particle. It is found that, with appropriately defined wavefunctions, this…
We provide a method to decompose the two-point function of a quantum field on a warped manifold in terms of fields living on a lower-dimensional manifold. We discuss explicit applications to Minkowski, de Sitter and anti-de Sitter quantum…
Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This…
The Covariant Phase Space Formalism (CPSF) provides a robust framework for deriving symplectic structures and surface charges in diffeomorphism-invariant theories. By construction, the CPSF operates on two distinct manifolds: the spacetime…
For a four dimensional, unitary, diffeomorphism- and scale invariant quantum field theory without higher derivatives and a well defined scale current we argue that scale invariance implies conformal invariance. The proof relies on the…
After the success of affine quantization in proving through Monte Carlo analysis that the covariant euclidean scalar field theory, $\varphi^r_n$, where $r$ denotes the power of the interaction term and $n = s + 1$ with $s$ the spatial…
Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review…
Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider…
We describe the space of (all) invariant deformation quantizations on the hyperbolic plane as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative…
A quantum sl(2,R) coalgebra is shown to underly the construction of a large class of superintegrable potentials on 3D curved spaces, that include the non-constant curvature analogues of the spherical, hyperbolic and (anti-)de Sitter spaces.…
These are notes on seminal work of Freed, and subsequent developments, on the curvature properties of (Sobolev Lie) groups of maps from a Riemannian manifold into a compact Lie group. We are mainly interested in critical cases which are…
We show that any conformal field theory in d-dimensional Minkowski space, in a phase with spontaneously broken conformal symmetry and with the dilaton among its fields, can be rewritten in terms of the static gauge (d-1)-brane on AdS_(d+1)…
A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a…