Related papers: Quantum field theory on a discrete space and nonco…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
Generally, quantum field theories can be thought as deformations away from conformal field theories. In this article, with a simple bottom up model assumed to possess a holographic description, we study a putative large N quantum field…
We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal…
Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…
The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds…
We do not know the symmetries underlying string theory. Furthermore, there must exist an inherently quantum, and spacetime independent, formulation of this theory. Independent of string theory, there should exist a description of quantum…
We construct an ultraviolet-complete, local, and unitary quantum field theory in 2+1 dimensions that exhibits spontaneous breaking of space-time parity, persisting to arbitrarily high temperatures. The theory is defined by a renormalization…
The connection between Lorentz invariance violation and noncommutativity of fields in a quantum field theory is investigated. A new dispersion relation for a free field theory with just one additional noncommutative parameter is obtained.…
We outline a field theory on a multifractal spacetime. The measure in the action is characterized by a varying Hausdorff dimension and logarithmic oscillations governed by a fundamental physical length. A fine hierarchy of length scales…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
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…
Noncommutative (NC) quantum field theory is the subject of many analyses on formal and general aspects looking for deviations and, therefore, potential noncommutative spacetime effects. Within of this large class, we may now pay some…
This monograph aims to build some new mathematical structures originated from Dyson--Schwinger equations for the description of non-perturbative aspects of gauge field theories whenever bare or running coupling constants are strong enough.
We consider a four-fermion theory as a simple model of dynamical symmetry breaking in flat space with non-trivial topology, motivated from recent studies in similar considerations in curved space. The phase structure is investigated, by…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather…
A class of quantum field theories invariant with respect to the action of an odd vector field Q on a source supermanifold $\Sigma$ is considered. We suppose that Q satisfies the conditions under which an integral of any Q-invariant function…