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Until recently little was known about the high-dimensional operators of the standard model effective field theory (SMEFT). However, in the past few years the number of these operators has been counted up to mass dimension 15 using…
The angular momentum formalism provides a powerful way to classify atomic states. Yet, requiring a spherical symmetry from the very first line, this formalism cannot be used for periodic systems, even though cubic semiconductor states are…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
Using bi-spinor fields we write the pseudo-scalar and bi-spinor fields that are characterized by the field functions of coordinates of several particles, namely multi-particle fields. By applying the quantization procedure to these…
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works.…
Much of the mathematical development of quantum field theory has been in support of determining the S-matrix in order to calculate scattering cross sections. However there is also an interest in determining how expectation values of field…
In this paper we try to prepare a framework for field quantization. To this end, we aim to replace the field of scalars R by self-adjoint elements of a commutative C-algebra, and reach an appropriate generalization of geometrical concepts…
This paper explores the long journey from projective tensor products of a pair of Banach spaces, passing through the definition of nuclear operators still on the realm of projective tensor products, to the of notion of trace-class operators…
We construct BRST operators for certain higher-spin extensions of the Virasoro algebra, in which there is a spin-$s$ gauge field on the world sheet, as well as the spin-2 gauge field corrresponding to the two-dimensional metric. We use…
We describe the ghost sector of cubic string field theory in terms of degrees of freedom on the two halves of a split string. In particular, we represent a class of pure ghost BRST operators as operators on the space of half-string…
We begin with a description of spacetime by a 4-dimensional cubic lattice $\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\sscripthat$…
Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in…
In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic…
We develop a theory of tensor categories over a field endowed with abstract operators. Our notion of a "field with operators", coming from work of Moosa and Scanlon, includes the familiar cases of differential and difference fields,…
Consider two free Hamiltonians for the same scalar field with two different masses. Wefind a squeeze operator which maps the ground state of one to the other. The operatoris described in both the Dirac and also the Schrodinger…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star,…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
Theory of $\tilde{J}$-pseudospin for $f$ element in cubic environment is developed. By fulfilling the symmetry requirements and the adiabatic connection to atomic limit, the crystal-field states are uniquely transformed into…