We give a unitary irreducible representation of the proper Poincar\'e group that leads to an operational version classical relativistic dynamics massive spinless particle. Unlike quantum mechanics, in this theory there is no uncertainty principle between position and momentum. It will be shown contains Koopman-von Neumann formalism as particular case, explicit connection with Hamiltonian mechan...

We show that there is a homotopy cofiber sequence of spectra relating Carlsson’s deformation K-theory of a group G to its “deformation representation ring,” analogous to the Bott periodicity sequence relating connective K-theory to ordinary homology. We then apply this to study simultaneous similarity of unitary matrices. The algebraic K-theory of a category uses the machinery of infinite loop ...

Recently A. Knapp [3] announced that every unitary principal series representation of a semisimple lie group decomposes simply; that is, no two distinct irreducible components of a given unitary principal series representation are equivalent. In proving this result Knapp analyzed in detail the structure of the spaces of intertwining operators for principal series representations. His analysis u...

Abstract Rubik’s Cube is one of the most famous combinatorial puzzles involving nearly 4.3 × 10 19 possible configurations. However, only a single configuration matches solved one. Its mathematical description expressed by group, whose elements define how its layers rotate. We develop unitary representation group and quantum formalism to describe based on geometrical constraints. Using particle...

Introduction: Two dimensional unitary transforms play an important role in image processing. The term image transform refers to a class of unitary matrices used for representation of images. In analogy with I-D signals that can be represented by an orthogonal series of basis functions, we can similarly represent an image in terms of a discrete set of basis arrays called “basis images ". These a...

We investigate the electronic transport through a single-level quantum-dot which is capacitively coupled to a charge-qubit. By employing the method of nonequilibrium Green's functions, we calculate the electric current through quantum dot at finite bias voltages. The Green's functions and self-energies of the system are calculated perturbatively and self-consistently to the second order of inte...

We analyze the hamiltonian quantization of Chern-Simons theory associated to the real group SL(2, C) R , universal covering of the Lorentz group SO(3, 1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological surface. Our main result is a construction of a unitary representation of this algebra. For this purpose we use the formalism of comb...