Related papers: Covariant Quantum Fields via Lorentz Group Represe…

We study homogeneous quantum L\'{e}vy processes and fields with independent additive increments over a noncommutative *-monoid. These are described by infinitely divisible generating state functionals, invariant with respect to an…

In the framework of (vector valued) quantized holomorphic functions defined on non-commutative spaces, ``quantized hermitian symmetric spaces'', we analyze what the algebras of quantized differential operators with variable coefficients…

In this work, we build a covariant basis for operators acting on the $(j,0)\oplus(0,j)$ Lorentz group representations. The construction is based on an analysis of the covariant properties of the parity operator, which for these…

We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the latter, we construct the corresponding polynomial analogue…

We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on…

It is shown in the present paper that the transformation relating a parallel transported vector in a Weyl space to the original one is the product of a multiplicative gauge transformation and a proper orthochronous Lorentz transformation.…

This is mainly a lecture note taken by myself following Weinberg's book, but also contains some corrections to the abuse of mathematical treatment. This article discusses projective unitary representations of Poincare group on the single…

We examine relationships between various quantization schemes for an electrically charged particle in the field of a magnetic monopole. Quantization maps are defined in invariant geometrical terms, appropriate to the case of nontrivial…

We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…

We show how the Weyl quantum walk derived from principles in Ref. [1], enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special…

It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and…

There is ambitious pretension formulated by Weinberg \cite{W} that {\it any relativistic quantum theory will look at sufficiently low energy like a quantum field theory.} It is based on the observation that for formulation of quantum field…

We introduce the notion of stochastic product as a binary operation on the convex set of quantum states (the density operators) that preserves the convex structure, and we investigate its main consequences. We consider, in particular,…

The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincar\'e group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson…

We perform a manifestly covariant quantization of a Weyl invariant, i.e., a locally scale invariant, scalar-tensor gravity in the extended de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance and a new…

Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current…

In our previous work [1] we described quantized computation using Horn clauses and based the semantics, dubbed as entanglement semantics as a generalization of denotational and distribution semantics, and founded it on quantum probability…

We introduce an extended class of cross-Toeplitz operators which act between Fock--Segal--Bargmann spaces with different weights. It is natural to consider these operators in the framework of representation theory of the Heisenberg group.…

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…

We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Hopf-Galois extension. Smash products of an algebra times a…