Related papers: The Operator Manifold Formalism. I
The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
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…
In this first part of the paper, we define a natural dual object for manifolds with corners and show how pseudodifferential calculus on such manifolds can be constructed in terms of the localization principle in C*-algebras. In the second…
The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose…
We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are…
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order…
We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be…
We show that Willwacher's cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a homotopy Gravity quasi-isomorphism…
This paper gives a concept of an integral operator defined on a manifold $M$ consisting of triple of points in $\mathbb{R}^{d}$ making up a regular $3$-simplex with the origin. The boundedness of such operator is investigated. The…
The structure of extended loop wave function is investigated in terms of the operator formalism. It is found that the extended loop wave function is characterized by the family number and classified by the partition of the family number. It…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
This note describes the functional-integral quantization of two-dimensional topological field theories together with applications to problems in deformation quantization of Poisson manifolds and reduction of certain submanifolds. A brief…
Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
We study cobordisms of a class of topological operads called ``manifold operads''. These operads are generalizations of the Fulton-MacPherson operad: an operad built from configurations of points in Euclidean space. Cobordism of manifold…