Related papers: Reeh-Schlieder Theorem for Ultrahyperfunctional Wi…
We prove that for a Wightman quantum field $\phi(x)$ the assumptions (i) positivity of the metric on the state space ${\cal H}$ of the theory (ii) the asymptotic condition in the form of Yang-Feldman equations and (iii) Klein-Gordon…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
This is the second in a series of two papers presenting a solution to Hilbert's 12th problem for real quadratic function fields in positive characteristic, in the sense of proving an analog of the Theorem of Weber-Fueter. We also offer a…
We discuss some aspects of noncommutative quantum field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. General properties of these theories are studied as well as the…
We give a definition of admissible counterterms appropriate for massive quantum field theories on the noncommutative Minkowski space, based on a suitable notion of locality. We then define products of fields of arbitrary order, the…
We present a generalization of Wigner's unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces.
Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely many inequivalent representations of the canonical commutator or anticommutator rings of field operators.…
We study the curvature condition which uniquely characterizes the hemisphere. In particular, we prove the Min-Oo conjecture for hypersurfaces in Euclidean space and hyperbolic space.
The nature and properties of the vacuum as well as the meaning and localization properties of one or many particle states have attracted a fair amount of attention and stirred up sometimes heated debate in relativistic quantum field theory…
An analogue of Rellich's theorem is proved for discrete Laplacian on square lattice, and applied to show unique continuation property on certain domains as well as non-existence of embedded eigenvalues for discrete Schr{\"o}dinger…
The Fock-Hilbert space generated by a single-particle interaction-free Wightman field is augmented by introducing non-trivial multi-particle (that is, multi-point, multilinear) quantum fields, which is justified insofar as Haag's theorem…
We study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field…
Quantum field theory (QFT) in Rindler spacetime is a gateway to understanding unitarity and information loss paradoxes in curved spacetime. Rindler coordinates map Minkowski spacetime onto regions with horizons, effectively dividing…
A corollary to the Reeh-Schlieder theorem is proved: that the time-ordered Vacuum Expectation Values and the S-matrix of a regularized Lagrangian quantum theory can be approximated by a local operator that uses nonlinear functionals of a…
A new generalized formulation of the spectral condition is proposed for quantum fields with highly singular infrared behavior whose vacuum correlation functions are well defined only under smearing with analytic test functions in momentum…
The state space and observables for the leading order of the large-N theory are constructed. The obtained model ("theory of infinite number of fields") is shown to obey Wightman-type axioms (including invariance under boost transformations)…
In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex…
We consider a quantum group interpretation of the non-anticommutative deformations in Euclidean supersymmetric theories. Twist deformations in the corresponding superspaces and Lie superalgebras are constructed in terms of the left…
Description of two three-dimensional topological quantum field theories of Witten type as twisted supersymmetric theories is presented. Low-energy effective action and a corresponding topological invariant of three-dimensional manifolds are…
For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the relation between a conserved `supercurrent' and the point-separated improved energy momentum tensor is investigated and a similar relation as on Minkowski space is…