相关论文: Quantum Mechanics of Extended Objects
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We study the quantization of a model proposed by Newton to explain centripetal force namely, that of a particle moving on a regular polygon. The exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a particle moving…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
In view of experimentally obtainable resolutions, equal to the Compton wavelength of an electron, the conventional interpretation of quantum mechanics no longer seems to provide a sufficiently subtle tool. Based on the intrinsic properties…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
We consider a gravitating extended object constructed from vacuum fluctuations of nonperturbatively quantized non-Abelian gauge fields. An approximate description of such an object is given by two gravitating scalar fields. The object has a…
We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a…
The quantum field theories (QFT) constructed in [1,2] include phenomenology of interest. The constructions approximate: scattering by $1/r$ and Yukawa potentials in non-relativistic approximations; and the first contributing order of the…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We show that Quantum Mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular Weyl affine space which we call Q-wis. This is proved using the Bohm-de Broglie causal formulation of Quantum…
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an…
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently…
In the present discussion Background Independent framework of Quantum Mechanics and its possible implications in the studies of gravity and Physics at short distance are addressed. The expression of the metric of quantum state space…
We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual…