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The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and…
By extending the method developed in our recent paper \cite{LM} we present the AQFT framework in terms of von Neumann algebras. In particular, this approach allows for a locally covariant categorical description of AQFT which moreover…
Electromagnetism is the paradigm case of a theory that satisfies relativistic locality. This can be proven by demonstrating that, once the theory's laws are imposed, what is happening within a region fixes what will happen in the…
Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic…
The dimension of any module over an algebra of affiliated operators ${\mathcal U}$ of a finite von Neumann algebra ${\mathcal A}$ is defined using a trace on ${\mathcal A}.$ All zero-dimensional ${\mathcal U}$-modules constitute the torsion…
We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be…
The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we…
The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in…
We consider the massive relativistic particle models on fourdimensional Minkowski space extended by $N$ commuting Weyl spinors for N=1 and N=2. The N=1 model is invariant under the most general form of bosonic counterpart of simple D=4…
We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic…
In this paper we consider properties of the space-time manifold M caused by the proposition that, according to the scheme theory, the manifold M is locally isomorphic to the spectrum of the algebra A, M = Spec(A), where A is the commutative…
A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal…
An examination is made of the way in which particles emerge from linear, bosonic, massive quantum field theories. Two different constructions of the one-particle subspace of such theories are given, both illustrating the importance of the…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
Current theories of massless free particle assume {\sl unitary} space inversion and {\sl anti-unitary} time reversal operators. In so doing robust classes of possible theories are discarded. In the present work theories of massless systems…
We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras A_V on the Minkowski half-plane M_+ starting with a local conformal net A of von Neumann algebras on the real line and an element V of…
We describe the free Dirac field in a four dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric…
Brunetti, Fredenhagen and Verch (BFV) have shown how the notion of local covariance for quantum field theories can be formulated in terms of category theory: a theory being described as a functor from a category of spacetimes to a category…
In bosonic JT gravity, minimally coupled to bulk matter, there exists a single, delta-function-normalisable state in each $SL(2,R)$ representation of the matter QFT for any pair of positive energies $E_L, E_R$ at the left and right…
The theory of free relativistic fields is shown to arise in a unified manner from higher-order, configuration-space, irreducible representations of the Poincar\'e group. A de Sitter subalgebra, in the massive case, and a Poincar\'e…