459 research outputs found
Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
We study the commutation relations, uncertainty relations and spectra of
position and momentum operators within the framework of quantum group %
symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an
effect of the underlying noncommutative geometry, a length and a momentum scale
appear, leading to the existence of minimal nonzero uncertainties in the
positions and momenta. The usual quantum mechanical behaviour is recovered as a
limiting case for not too small and not too large distances and momenta.Comment: 15 pages, Latex, preprint DAMTP/93-6
Classification of quantum relativistic orientable objects
Started from our work "Fields on the Poincare Group and Quantum Description
of Orientable Objects" (EPJC,2009), we consider here a classification of
orientable relativistic quantum objects in 3+1 dimensions. In such a
classification, one uses a maximal set of 10 commuting operators (generators of
left and right transformations) in the space of functions on the Poincare
group. In addition to usual 6 quantum numbers related to external symmetries
(given by left generators), there appear additional quantum numbers related to
internal symmetries (given by right generators). We believe that the proposed
approach can be useful for description of elementary spinning particles
considering as orientable objects. In particular, their classification in the
framework of the approach under consideration reproduces the usual
classification but is more comprehensive. This allows one to give a
group-theoretical interpretation to some facts of the existing phenomenological
classification of known spinning particles.Comment: 24 page
On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
We continue studies on quantum field theories on noncommutative geometric
spaces, focusing on classes of noncommutative geometries which imply
ultraviolet and infrared modifications in the form of nonzero minimal
uncertainties in positions and momenta. The case of the ultraviolet modified
uncertainty relation which has appeared from string theory and quantum gravity
is covered. The example of euclidean -theory is studied in detail and
in this example we can now show ultraviolet and infrared regularisation of all
graphs.Comment: LaTex, 32 page
Hyperspherical harmonics with arbitrary arguments
The derivation scheme for hyperspherical harmonics (HSH) with arbitrary
arguments is proposed. It is demonstrated that HSH can be presented as the
product of HSH corresponding to spaces with lower dimensionality multiplied by
the orthogonal (Jacobi or Gegenbauer) polynomial. The relation of HSH to
quantum few-body problems is discussed. The explicit expressions for
orthonormal HSH in spaces with dimensions from 2 to 6 are given. The important
particular cases of four- and six-dimensional spaces are analyzed in detail and
explicit expressions for HSH are given for several choices of hyperangles. In
the six-dimensional space, HSH representing the kinetic energy operator
corresponding to i) the three-body problem in physical space and ii) four-body
planar problem are derived.Comment: 18 pages, 1 figur
Symmetric coupling of four spin-1/2 systems
We address the non-binary coupling of identical angular momenta based upon
the representation theory for the symmetric group. A correspondence is pointed
out between the complete set of commuting operators and the
reference-frame-free subsystems. We provide a detailed analysis of the coupling
of three and four spin-1/2 systems and discuss a symmetric coupling of four
spin-1/2 systems.Comment: 20 pages, no figure
Semiclassical Analysis of the Wigner Symbol with One Small Angular Momentum
We derive an asymptotic formula for the Wigner symbol, in the limit of
one small and 11 large angular momenta. There are two kinds of asymptotic
formulas for the symbol with one small angular momentum. We present the
first kind of formula in this paper. Our derivation relies on the techniques
developed in the semiclassical analysis of the Wigner symbol [L. Yu and R.
G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant
form of the multicomponent WKB wave-functions to derive asymptotic formulas for
the symbol with small and large angular momenta. When applying the same
technique to the symbol in this paper, we find that the spinor is
diagonalized in the direction of an intermediate angular momentum. In addition,
we find that the geometry of the derived asymptotic formula for the
symbol is expressed in terms of the vector diagram for a symbol. This
illustrates a general geometric connection between asymptotic limits of the
various symbols. This work contributes the first known asymptotic formula
for the symbol to the quantum theory of angular momentum, and serves as a
basis for finding asymptotic formulas for the Wigner symbol with two
small angular momenta.Comment: 15 pages, 14 figure
A q-Deformed Schr\"odinger Equation
We found hermitian realizations of the position vector , the angular
momentum and the linear momentum , all behaving like
vectors under the algebra, generated by and . They are
used to introduce a -deformed Schr\" odinger equation. Its solutions for the
particular cases of the Coulomb and the harmonic oscillator potentials are
given and briefly discussed.Comment: 14 pages, latex, no figure
Characterisations of Classical and Non-classical states of Quantised Radiation
A new operator based condition for distinguishing classical from
non-classical states of quantised radiation is developed. It exploits the fact
that the normal ordering rule of correspondence to go from classical to quantum
dynamical variables does not in general maintain positivity. It is shown that
the approach naturally leads to distinguishing several layers of increasing
nonclassicality, with more layers as the number of modes increases. A
generalisation of the notion of subpoissonian statistics for two-mode radiation
fields is achieved by analysing completely all correlations and fluctuations in
quadratic combinations of mode annihilation and creation operators conserving
the total photon number. This generalisation is nontrivial and intrinsically
two-mode as it goes beyond all possible single mode projections of the two-mode
field. The nonclassicality of pair coherent states, squeezed vacuum and
squeezed thermal states is analysed and contrasted with one another, comparing
the generalised subpoissonian statistics with extant signatures of nonclassical
behaviour.Comment: 16 pages, Revtex, One postscript Figure compressed and uuencoded
Replaced, minor changes in eq 4.30 and 4.32. no effect on the result
Evolution of a spinor condensate: coherent dynamics, dephasing and revivals
We present measurements and a theoretical model for the interplay of spin
dependent interactions and external magnetic fields in atomic spinor
condensates. We highlight general features like quadratic Zeeman dephasing and
its influence on coherent spin mixing processes by focusing on a specific
coherent superposition state in a F=1 Rb Bose-Einstein condensate. In
particular, we observe the transition from coherent spinor oscillations to
thermal equilibration
Structure Constants for New Infinite-Dimensional Lie Algebras of U(N+,N-) Tensor Operators and Applications
The structure constants for Moyal brackets of an infinite basis of functions
on the algebraic manifolds M of pseudo-unitary groups U(N_+,N_-) are provided.
They generalize the Virasoro and W_\infty algebras to higher dimensions. The
connection with volume-preserving diffeomorphisms on M, higher generalized-spin
and tensor operator algebras of U(N_+,N_-) is discussed. These
centrally-extended, infinite-dimensional Lie-algebras provide also the arena
for non-linear integrable field theories in higher dimensions, residual gauge
symmetries of higher-extended objects in the light-cone gauge and C^*-algebras
for tractable non-commutative versions of symmetric curved spaces.Comment: 8 pages, LaTeX, no figures; minor comments added; to appear in J.
Phys A (Math. Gen.
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