2,296 research outputs found
On Finite Noncommutativity in Quantum Field Theory
We consider various modifications of the Weyl-Moyal star-product, in order to
obtain a finite range of nonlocality. The basic requirements are to preserve
the commutation relations of the coordinates as well as the associativity of
the new product. We show that a modification of the differential representation
of the Weyl-Moyal star-product by an exponential function of derivatives will
not lead to a finite range of nonlocality. We also modify the integral kernel
of the star-product introducing a Gaussian damping, but find a nonassociative
product which remains infinitely nonlocal. We are therefore led to propose that
the Weyl-Moyal product should be modified by a cutoff like function, in order
to remove the infinite nonlocality of the product. We provide such a product,
but it appears that one has to abandon the possibility of analytic calculation
with the new product.Comment: 13 pages, reference adde
Charge and potential distributions for particles approaching substrates with regular structures
The charge and potential distributions for insulating particles approaching a
substrate with regular insulating structures are studied by particle-in-cell
numerical simulations. An elongated particle and substrate with elongated
structures are considered for flowing plasmas. The role of the relative
position of the particle and the substrate in their interactions is
investigated. It is also demonstrated that the interactions are modified by
photoemission due to directed UV light. The simulations are two dimensional
with ions and electrons treated as individual particles.Comment: 5 pages, submitted to IEEE Trans Plasma Sc
The fundamental solution of the unidirectional pulse propagation equation
The fundamental solution of a variant of the three-dimensional wave equation
known as "unidirectional pulse propagation equation" (UPPE) and its paraxial
approximation is obtained. It is shown that the fundamental solution can be
presented as a projection of a fundamental solution of the wave equation to
some functional subspace. We discuss the degree of equivalence of the UPPE and
the wave equation in this respect. In particular, we show that the UPPE, in
contrast to the common belief, describes wave propagation in both longitudinal
and temporal directions, and, thereby, its fundamental solution possesses a
non-causal character.Comment: accepted to J. Math. Phy
Fuzzy Geometry of Phase Space and Quantization of Massive Fields
The quantum space-time and the phase space with fuzzy structure is
investigated as the possible quantization formalism. In this theory the state
of nonrelativistic particle corresponds to the element of fuzzy ordered set
(Foset) - fuzzy point. Due to Foset partial (weak) ordering, particle's space
coordinate x acquires principal uncertainty dx. It's shown that Shroedinger
formalism of Quantum Mechanics can be completely derived from consideration of
particle evolution in fuzzy phase space with minimal number of axioms.Comment: 13 pages, Talk given at QFEXT07 Workshop, Leipzig, Sept. 200
Discretized rotation has infinitely many periodic orbits
For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by
(x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic
orbits.Comment: Revised after referee reports, and added a quantitative statemen
p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency
The classical and quantum formalism for a p-adic and adelic harmonic
oscillator with time-dependent frequency is developed, and general formulae for
main theoretical quantities are obtained. In particular, the p-adic propagator
is calculated, and the existence of a simple vacuum state as well as adelic
quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical
phase are noted.Comment: 10 page
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These
versions are applicable to Laplace transforms of Schwartz distributions. We
apply these Tauberian results to deduce a number of Tauberian theorems for
power series where Ces\`{a}ro summability follows from Abel summability. We
also use our general results to give a new simple proof of the classical
Littlewood one-sided Tauberian theorem for power series.Comment: 15 page
Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold
We derive non-linear recursion equation for the leading infrared logarithms
(LL) in four dimensional sigma-model with fields on an arbitrary Riemann
manifold. The derived equation allows one to compute leading infrared
logarithms to essentially unlimited loop order in terms of geometric
characteristics of the Riemann manifold.
We reduce the solution of the SU(oo) principal chiral field in arbitrary
number of dimensions in the LL approximation to the solution of very simple
recursive equation. This result paves a way to the solution of the model in
arbitrary number of dimensions at N-->ooComment: Talk given by MVP at the conference devoted to memory of A.N.
Vasilie
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