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The definition of the standard differential operator is extended from integer steps to arbitrary stepsize. The classical, nonrelativistic Hamiltonian is quantized, using these new continuous operators. The resulting Schroedinger type…
The Moyal star formulation of string field theory is reviewed. The various versions of the star product are compared and related to one another in a regulated theory that resolves associativity anomalies. A summary of computations and…
Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are…
The string bracket introduced by Chas and Sullivan [math.GT/9911159] is reinterpreted from the point of view of topological field theories in the Batalin-Vilkovisky or BRST formalisms. Namely, topological action functionals for gauge fields…
The set C of complex-valued continuous functions on [0,\infty) is a ring by the addition and the convolution. It has the quotient field Q(C), by which J. Mikusinski developed his operational calculus. In this paper, we revisit a derivation…
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…
While multifractal spectra are convex, general field theoretic arguments show that power of field operators $\phi^f$ yield a concave spectrum of exponents as function of $f$. This is resolved by appropriate choice of operators to describe…
Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values…
A general semiclassical theory for the calculation of reaction rate constants is developed. The theory can be understood as a formal framework that encompasses existing semiclassical methods: instanton theory and semiclassical transition…
An introduction and survey is given of some recent work on the infinitesimal dynamics of \textit{crystal frameworks}, that is, of translationally periodic discrete bond-node structures in $\mathbb{R}^d$, for $ d=2,3,...$. We discuss the…
Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first…
Since the discovery a century ago, spin describing the intrinsic angular momentum of massive elementary particles has exposed its nature and significant roles in wide ranges of (relativistic) quantum phenomena and practical applications for…
We establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, (off-shell) level-matched closed string states are represented by star algebra projectors in open…
The physically correct parametrization of the energy levels of transition ions in crystals in terms of crystal-field (CF) Hamiltonians ${\cal H}_{\rm CF}=\sum_{k}\sum_{q}B_{kq}C_{q}^{(k)}$ has to be based on the CF parameters $B_{kq}$ that…
The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…
We present a new approach to computing multiplets for core spectroscopies, whereby the crystal field is constructed explicitly from the positions and charges of surrounding atoms. The simplicity of the input allows the consideration of…
In this paper we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is understood as an interpretation of concrete differential operators…
We describe how to define observables analogous to quantum fields for the semicontinuous limit recently introduced by Jones in the study of unitary representations of Thompson's groups $F$ and $T$. We find that, in terms of correlation…
Given two conformal field theories related to each other by a marginal perturbation, and string field theories constructed around such backgrounds, we show how to construct explicit redefinition of string fields which relate these two…
The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended for a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The…