Related papers: Note on Plane Wave Quantum Mechanics
We extend the formalism of Hamiltonian string bit models of quantum gravity type in two spacetime dimensions to include couplings to particles. We find that the single-particle closed and open universe models respectively behave like empty…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space -- time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent,…
We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding…
We reconsider the quantum vacuum interaction energy between two straight parallel cosmic strings. This problem was discussed several times in an approach treating both strings perturbatively and treating only one perturbatively. Here we…
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing…
We construct the string states $|O_{p}^J>_J$, $|O_{q}^{J_1}>_{{J_1}{J_2}}$ and $|O_{0}^{J_{1}J_{2}}>_{{J_1}{J_2}}$ in the Hilbert space of the quantum mechanical orbifold model so as to calculate the three point functions and the matrix…
We study the non-singlet sectors of matrix quantum mechanics (MQM) through an operator algebra which generates the spectrum. The algebra is a nonlinear extension of the W_\infty algebra where the nonlinearity comes from the angular part of…
We consider potential scattering theory of a nonrelativistic quantum mechanical 2-particle system in R^2 with anyon statistics. Sufficient conditions are given which guarantee the existence of wave operators and the unitarity of the…
For a class of negative slowly decaying potentials, including $V(x):=-\gamma|x|^{-\mu}$ with $0<\mu<2$, we study the quantum mechanical scattering theory in the low-energy regime. Using modifiers of the Isozaki-Kitada type we show that…
We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$.…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of…
We study the Schroedinger operators H_{\lambda\mu}(K), with K \in T_2 the fixed quasi-momentum of the particles pair, associated with a system of two identical fermions on the two-dimensional lattice Z_2 with first and second…
This paper concerns instanton contributions to two-point correlation functions of BMN operators in N=4 supersymmetric Yang-Mills that vanish in planar perturbation theory. Two-point functions of operators with even numbers of fermionic…
We systematically investigate open strings in the plane wave background of type IIB string theory. We carefully analyze possible boundary conditions for open strings and find static as well as time-dependent branes. The branes fall into…
We consider branes in refined topological strings. We argue that their wave-functions satisfy a Schr\"odinger equation depending on multiple times and prove this in the case where the topological string has a dual matrix model description.…
In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct…
Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. In this letter we present a general method based on quantum tomography for…
In type IIB light-cone superstring field theory, the cubic interaction has two pieces: a delta-functional overlap and an operator inserted at the interaction point. In this paper we extend our earlier work hep-th/0204146 by computing the…