Related papers: Paths with singularities in functional integrals o…
We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as…
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the…
Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the…
The concept of unified field theory is discussed. Two nonlinear field models with world volume type action are considered, namely extremal space-time film model and Born -- Infeld nonlinear electrodynamics. The natural appearance of two…
First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The…
A free-theory vacuum state of an interacting field theory, e.g. quantum gravity, is unstable at tree level in general due to spontaneous emission of Fock-space particles in any spacetime with no global timelike Killing vectors, such as de…
We construct examples of Functorial Quantum Field Theories in the Riemannian setting by quantizing free massive bosons.
A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative…
We discuss quantum theory of fields \phi defined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which is a bilinear form in \phi defines the Gaussian measure with a covariance (Green function)…
Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of cobordisms and (commutative) Frobenius…
In classical function theory, a function is holomorphic if and only if it is complex analytic. For higher dimensional spaces it is natural to work in the context of Clifford algebras. The structures of these algebras depend on the parity of…
It is argued that substantial portions of both Newtonian particle mechanics and general relativity can be viewed as relational (rather than absolute) theories. I furthermore use the relational particle models as toy models to investigate…
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical…
I recall the main motivation to study quantum field theories on noncommutative spaces and comment on the most-studied example, the noncommutative R^4. That algebra is given by the *-product which can be written in (at least) two ways: in an…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
We analyze quantum field theories on spacetimes $M$ with timelike boundary from a model-independent perspective. We construct an adjunction which describes a universal extension to the whole spacetime $M$ of theories defined only on the…
We develop an approach to investigate the non-perturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field…
When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path…
Currently, some approaches to the associated Legendre functions based on different factorization methods are known. However, they have not allowed identifying new properties that permit to improve our knowledge of any physical system. In…
We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral…