Related papers: The quadratic Fock functor
In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…
We characterize the category of co-semi-analytic functors and describe an action of semi-analytic functors on co-semi-analytic functors.
In this paper, we consider the groupoidification of the fermion algebra. We construct a groupoid as the categorical analogues of the fermionic Fock space, and the creation and annihilation operators correspond to spans of groupoids. The…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental…
Every right adjoint functor between presentable $\infty$-categories is shown to decompose canonically as a coreflection, followed by, possibly transfinitely many, monadic functors. Furthermore, the coreflection part is given a presentation…
This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split…
For a category B with finite products, we first characterize pseudofunctors from B to Cat whose corresponding opfibration is cartesian monoidal. Among those, we then characterize the ones which extend to pseudofunctors from internal groups…
We extend the inner product from bosonic Fock space to a pairing between suitable antifunctionals on the symmetric algebra. Our account is illustrated by the (Gaussian) half-form pairing between positive polarizations in the form needed for…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
We define a unified categorical framework for studying six subproblems arising from the classical Four Subspace Problem. For each subproblem, we construct a functor from its associated category to the category of representations of the…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…
We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter ${\tilde{\nu}}=\nu+1$ which is…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
The article proposes the description of internal spaces of fermion (quarks and leptons and antiquarks and antileptons) and boson (photons, weak bosons, gluons, gravitons and scalars) second quantized fields in a unique way if they all are…