Related papers: New Examples for Wightman Fields on a Manifold
Large $N$ two-dimensional QCD on a cylinder and on a vertex manifold (a sphere with three holes) is investigated. The relation between the saddle-point description and the collective field theory of QCD$_2$ is established. Using this…
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete…
It is shown that multilinear Calder\'on-Zygmund operators are bounded on products of Hardy spaces.
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define…
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of…
The space, on which quantum field operators are given, is constructed in any theory, in which the usual product between test functions is substituted by the $\star$-product (the Moyal-type product). The important example of such a theory is…
Point splitting has been suggested as a way to deal with anomalous commutators in quantum field theory. It has been pointed out by D.G. Boulware[4] that in order to obtain a mathematically consistent theory the Hamiltonian operator must be…
In this paper, we study a free scalar field in a specific (1+1)-dimensional curved spacetime. By introducing an algebraic state that is locally Hadamard, we derive the renormalized Wightman function and explicitly calculate the covariantly…
Grassmann variables are used to formally transform a system with constraints into an unconstrained system. As a result, the Schr\"{o}dinger equation arises instead of the Wheeler-DeWitt one. The Schr\"{o}dinger equation describes a system's…
An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose second symmetric porduct is the Hilbert cube. A factor theorem is given for nth symmetric product of the cartesian product of any absolute…
The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces…
We study the scattering dynamics of an $n$-component spinor wavefunction in a random environment on a two-dimensional lattice. In the presence of particle-hole symmetry we find diffusion on large scales. The latter is described by a…
We give a finite dimensional approach to the Chas-Sullivan product on the free loop space of a manifold, orientable or not.
In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of…
This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical…
In this work we study the presence of kinks in models described by two real scalar fields in bi-dimensional space-time. We generate new two-field models, constructed from distinct but important one-field models, and we solve them with…
Let $S$ be a smooth projective surface over $\mathbb{C}$ and $S^{[n]}$ be the Hilbert scheme of $n$ points over $S$, for any positive integer $n$. Let ${\bf a}=(n_1,\ldots,n_r)$ and ${\bf b}=(m_1,\ldots,m_s)$ be two distinct partitions of…
It is observed that certain convex envelopes of Wightman type functionals corresponding to scalar, stochastically positive quantum fields consist of Wightman type functionals only .This leads to the construction of a large classes of not…
We describe a representation of the $q$--hypergeometric functions of one variable in terms of correlators of vertex operators made out of free scalar fields on the Riemann sphere.