1,721,012 research outputs found
Ultraviolet finiteness of the averaged Hamiltonian on the noncommutative Minkowski space
No full textIt is shown that the Hamiltonian approach for a ϕ3-interaction on the 4-dimensional noncommutative Minkowski space leads to an ultraviolet finite S-matrix if the noncommutativity is averaged at each vertex
The ultraviolet infrared mixing problem on the noncommutative Moyal space
No full textIt is shown that the mixing of ultraviolet and infrared divergences in quantum field theory on Moyal space is not an artefact of the Euclidean framework, but occurs also in the Hamiltonian setting when the interaction is given in terms of the Moyal twisted convolution product. The mixing mechanism in both settings is examined from the point of view of microlocal analysis and it is shown that they are different from one another
The ultraviolet infrared mixing problem on the noncommutative Moyal space
No full textIt is shown that the mixing of ultraviolet and infrared divergences in quantum field theory on Moyal space is not an artefact of the Euclidean framework, but occurs also in the Hamiltonian setting when the interaction is given in terms of the Moyal twisted convolution product. The mixing mechanism in both settings is examined from the point of view of microlocal analysis and it is shown that they are different from one another
The shuffle Hopf algebra and quasiplanar Wick products
No full textThe operator valued distributions which arise in quantum field theory on the noncommutative Minkowski space can be symbolized by a generalization of chord diagrams, the dotted chord diagrams. In this framework, the combinatorial aspects of quasiplanar Wick products are understood in terms of the shuffle Hopf algebra of dotted chord diagrams, leading to an algebraic characterization of quasiplanar Wick products as a convolution. Moreover, it is shown that the distributions do not provide a weight system for universal knot invariants
Ultraviolet finiteness of the averaged Hamiltonian on the noncommutative Minkowski space
No full textIt is shown that the Hamiltonian approach for a ϕ3-interaction on the 4-dimensional noncommutative Minkowski space leads to an ultraviolet finite S-matrix if the noncommutativity is averaged at each vertex
The invariant charges of the Nambu–Goto string and canonical quantization
No full textIt is shown that the algebra of diffeomorphism-invariant charges of the Nambu–Goto string cannot be quantized in the framework of canonical quantization. The argument is shown to be independent of the dimension of the underlying Minkowski space
Schwinger Functions in Noncommutative Quantum Field Theory
Full text linkIt is shown that the ehBpoint functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from renormalization in the Minkowskian regime
An ultraviolet‐finite Hamiltonian approach on the noncommutative Minkowski space
No full textWritten version of a talk presented at the 36th International Symposium Ahrenshoop on the Theory of Elementary Particles, 26-30 August 2003, Wernsdorf, Germany. This is an exposition of joint work with S. Doplicher, K. Fredenhagen, and G. Piacitelli on field theory on the noncommutative Minkowski space [1]. The limit of coinciding points is modified compared to ordinary field theory in a suitable way which allows for the definition of so-called regularized field monomials as interaction terms. Employing these in the Hamiltonian formalism results in an ultraviolet finite S-matrix
On-shell Extension of Distributions
No full textWe consider distributions on Rn∖{0} which satisfy a given set of partial differential equations and provide criteria for the existence of extensions to Rn that satisfy the same set of equations on Rn. We use the results to construct distributions satisfying specific renormalisation conditions in the Epstein and Glaser approach to perturbative quantum field theory. Contrary to other approaches, we provide a unified approach to treat Lorentz covariance, invariance under global gauge group and almost homogeneity, as well as discrete symmetries. We show that all such symmetries can be recovered by applying a linear map defined for all degrees of divergence. Using similar techniques, we find a relation between on-shell and off-shell time-ordered products involving higher derivatives of the fields
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