Related papers: Many-fermion wave functions: structure and example…
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…
The effects of two distinct operations of the elements of the symmetry groups of a Hamiltonian on a quantum state might be equivalent in some specific zones of coordinate space. Making use of the matrix representations of the groups, the…
We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the hydrogen chromophore's vibrational motion in the molecule $CF_3CHFI$. The original model has 4 degrees of freedom, three positions and one representing…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
It is shown how to exactly simulate many-body interactions and multi-qubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a…
Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field…
Quantum Algebras (q-algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and…
We present a geometrical way of understanding the dynamics of wavefunctions in a free space, using the phase-space formulation of quantum mechanics. By visualizing the Wigner function, the spreading, shearing, the so-called "negative…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
Gleason's theorem asserts the equivalence of von Neumann's density operator formalism of quantum mechanics and frame functions, which are functions on the pure states that sum to 1 on any orthonormal basis of Hilbert space of dimension at…
Spontaneous symmetry breaking is examined by regarding it as a phenomenon in the eternal intermediate state due to sequential perturbations. The concept of the relativistic many-body state is applied to this intermediate state occurring in…
A geometric interpretation for an algebraic interacting boson-fermion model with configuration mixing is presented. The formalism is based on an extended Bose-Fermi matrix coherent states and is applied to gain insight on intertwined…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…
When a quantum particle moves in a curved space, a geometric potential can arise. In spite of a long history of extensive theoretical studies, to experimentally observe the geometric potential remains to be a challenge. What are the…
Let $G$ be a semisimple Lie group, ${\frak g}$ its Lie algebra. For any symmetric space $M$ over $G$ we construct a new (deformed) multiplication in the space $A$ of smooth functions on $M$. This multiplication is invariant under the action…
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them…
We realize the Weil representation of infinite dimensional symplectic group and spinor representation of infinite-dimensional group $GL$ by linear operators in the space of symmetric functions in infinite number of variables.