Related papers: Perturbation theory in (2,2) signature
The non-commutative version of the euclidean $g^2\phi^4$ theory is considered. By using Wilsonian flow equations the ultraviolet renormalizability can be proved to all orders in perturbation theory. On the other hand, the infrared sector…
Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory…
A new bootstrap equation in 2-dimensional conformal field theory is derived starting from the momentum-space representation of the correlation functions. Since Wightman functions are not crossing-symmetric, the analyticity properties of the…
Four-dimensional quantum electrodynamics has been formulated on a hypercubic Minkowski finite-element lattice. The equations of motion have been derived so as to preserve lattice gauge invariance and have been shown to be unitary. In…
Four-dimensional gauge theories with matter can have regions in parameter space, often dubbed conformal windows, where they flow in the infrared to non-trivial conformal field theories. It has been conjectured that conformality can be lost…
In vacuum, the world-line formalism is an efficient tool for calculating observables in the presence of arbitrary constant external fields. The natural frame of this formalism is the Euclidean space. At finite temperature the analytic…
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large…
Positive definiteness of a Hamiltonian expanded about an equilibrium point provides only a necessary condition for stability, a criterion known as Dirichlet's theorem. The reason that this criterion is not necessary for stability is because…
Permutations of particle labels are usually used to illustrate the relationship between classical and quantum statistics. We use permutations of attributes/properties of particles to express properties of waves. We express events of the…
We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…
In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…
Nonlinear deformations of relativistic symmetries at the Planck scale are usually addressed in terms of modified dispersion relations. We explore here an alternative route by directly deforming the two-point functions of an underlying field…
Using the twist deformation of $U(igl(4,R))$, the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional $\kappa$-Minkowski spacetime. The action in momentum space turns…
We generalize the worldline variational approach to field theory by introducing a trial action which allows for anisotropic terms to be induced by external 4-momenta of Green's functions. By solving the ensuing variational equations…
Perturbation theory for a class of topological field theories containing antisymmetric tensor fields is considered. These models are characterized by a supersymmetric structure which allows to establish their perturbative finiteness.
The perturbative expansion of Chern-Simons gauge theory leads to invariants of knots and links, the finite type invariants or Vassiliev invariants. It has been proven that at any order in perturbation theory the resulting expression is an…
A new method is presented for the simplification of loop integrals in one particle irreducible diagrams with large numbers of external lines, based on the partial fractioning of products of propagators. Whenever a loop diagram in $d$…
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature…
The stability of the fundamental defects of an unstretchable flat sheet is examined. This involves expanding the bending energy to second order in deformations about the defect. The modes of deformation occur as eigenstates of a…