Related papers: Towards an Axiomatic Formulation of Noncommutative…
The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…
For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
It will be shown that the Reeh-Schlieder property holds for states of quantum fields for ultrahyperfunctional Wightman theory. As by product, it is shown that the Reeh-Schlieder property also holds for states of quantum fields on a…
We show that despite the inherent non-locality of quantum field theories on the Groenewold-Moyal (GM) plane, one can find a class of ${\bf C}$, ${\bf P}$, ${\bf T}$ and ${\bf CPT}$ invariant theories. In particular, these are theories…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
We formulate Noncommutative Qauntum Field Theory in terms of fields defined as mean value over coherent states of the noncommutative plane. No *-product is needed in this formulation and noncommutativity is carried by a modified Fourier…
The problem of gauge invariance in an ultraviolet complete quantum field theory (QFT) with nonlocal interactions is investigated. For local fields that couple through a nonlocal interaction, it is demonstrated that the quantum…
We point out that quantum field theories based on the concept of Clifford space and Clifford algebra valued-fields involve both positive and negative energies. This is a consequence of the indefinite signature (p,q) of the Clifford space.…
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…
It is argued that the severe consequences of Haag's inconsistency theorem for relativistic quantum field theories can be successfully evaded in the direct-action approach. Some recent favorable comments of John Wheeler, often mistakenly…
Higher order terms in the effective action of noncommutative gauge theories exhibit generalizations of the *-product (e.g. *' and *-3). These terms do not manifestly respect the noncommutative gauge invariance of the tree level action. In…
In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3) group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the…
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…
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…
This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge…
Inspired by the structural unification of unitary groups (quantum field theory) with orthogonal groups (relativity) proposed recently through a non-division algebra, we construct a hypercomplex field theory with an internal symmetry that…
Axiomatic quantum field theory (QFT) provides a rigorous mathematical foundation for QFT, and it is the basis for proving some important general results, such as the well-known spin-statistics theorem. Free-field QFT meets the axioms of…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…