Related papers: Quantum Mechanics on S^n and Meron Solution
Having started with the general formulation of the quantum theory of the real scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the general--covariant quasinonrelativistic quantum mechanics of a point-like spinless…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the K\"ahler form with jumps…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
A topological theory for the interactions in Nature is presented. The theory derives from the cyclic properties of the topological manifold Q=2T^3 + 3S^1 x S^2 which has 23 intrinsic degrees of freedom, discrete Z_3 and Z_2 x Z_3 internal…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a…
The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the…
Since the Maxwell theory of electromagnetic phenomena is a gauge theory, it is quite important to evaluate the zero-point energy of the quantized electromagnetic field by a careful assignment of boundary conditions on the potential and on…
Topological properties of quantum system is directly associated with the wave function. Based on the decomposition theory of gauge potential, a new comprehension of topological quantum mechanics is discussed. One shows that a topological…
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3 \equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient isotopic…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge field. In leading order approximation,…
We show that the inclusion of the monopole field in the three- and five-dimensional spherically symmetric quantum mechanical systems, supplied by the addition of the special centrifugal term, does not yield any change in the radial…
A gauge theory with an indefinite metric without negative probabilities is given by extending quantum mechanics, where a general metric is introduced, and the invariance under the general linear transformation is imposed on the space of…
We present a gauge-invariant treatment of singularity resolution using loop quantum gravity techniques with respect to local SU(2) transformations. Our analysis reveals many novel features of quantum geometry which were till now hidden in…
We consider the Einstein-Yang-Mills-Higgs equations for an SU(3) gauge group in a spherically symmetric ansatz. Several properties of the gravitating monopole solutions are obtained an compared with their SU(2) counterpart.
When a dyon encircles an infinitely-long solenoid enclosing uniform electric and magnetic fields, its wave function accumulates a duality-invariant quantum phase, which is topological because it depends on a winding number and is nonlocal…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…