Related papers: Algebraic quantum field theory: objectives, method…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
Quantum field theory at finite temperature and density can be used for describing the physics of relativistic plasmas. Such systems are frequently encountered in astrophysical situations, such as the early Universe, Supernova explosions,…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field…
A general framework of non-perturbative quantum field theory on a curved background is presented. A quantum field theory is in this setting characterised by an embedding of a space of field configurations into a Hilbert space over…
We present a unified approach to holomorphic anomaly equations and some well-known quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the Deligne-Mumford moduli spaces…
We review the mathematically rigorous formulation of the quantum theory of a linear field propagating in a globally hyperbolic spacetime. This formulation is accomplished via the algebraic approach, which, in essence, simultaneously admits…