Related papers: On Function Theory in Quantum Disc: Covariance
The q-monopole bundle introduced previously is extended to a general construction for quantum group bundles with non-universal differential calculi. We show that the theory applies to several other classes of bundles as well, including…
The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal…
In the area of the foundations of quantum mechanics a true industry appears to have developed in the last decades, with the aim of proving as many results as possible concerning what there cannot be in the quantum realm. In principle, the…
A quantum electrodynamical time-dependent density functional theory framework is applied to describe strongly coupled light--matter interactions in cavity environments. The formalism utilizes a tensor product approach, coupling real-space…
Quantum theory was radically different from the theories of nature which came before it. One key difference was its use of complex numbers. This opened a longstanding debate over whether quantum theory fundamentally requires complex numbers…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
We suggest a new strategy for proving large $N$ duality by interpreting Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function. For the resolved…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
The work is a concept of fundamental importance in thermodynamics. An open question is how to describe the work fluctuation for quantum coherent processes in the presence of initial quantum coherence in the energy basis. With the aim of…
We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
The particle algebras generated by the creation/annihilation operators for bosons and for fermions are shown to possess quantum invariance groups. These structures and their sub(quantum)groups are investigated.
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn't break general covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda) and extremely…
The similarity transformations of quantum orthogonal groups are developed and FRT theory is reformulated to the Cartesian basis. The quantum orthogonal Cayley-Klein groups are introduced as the algebra functions over an associative algebra…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
A motivation comes from {\em M. Ismail and et al.: A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77--84} to study a generalization of close-to-convex functions by means of a $q$-analog of a difference…