114 research outputs found
coherent state operators and invariant correlation functions and their quantum group counterparts
Coherent state operators (CSO) are defined as operator valued functions on
G=SL(n,C), homogeneous with respect to right multiplication by lower triangular
matrices. They act on a model space containing all holomorphic finite
dimensional representations of G with multiplicity 1. CSO provide an analytic
tool for studying G invariant 2- and 3-point functions, which are written down
in the case of . The quantum group deformation of the construction gives
rise to a non-commutative coset space. We introduce a "standard" polynomial
basis in this space (related to but not identical with the Lusztig canonical
basis) which is appropriate for writing down invariant 2-point
functions for representaions of the type and .
General invariant 2-point functions are written down in a mixed
Poincar\'e-Birkhoff-Witt type basis.Comment: 33 pages, LATEX, preprint IPNO/TH 94-0
Quantum mechanics on Hilbert manifolds: The principle of functional relativity
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold.
Images of charts on the manifold are allowed to belong to arbitrary Hilbert
spaces of functions including spaces of generalized functions. Tensor equations
in this setting, also called functional tensor equations, describe families of
functional equations on various Hilbert spaces of functions. The principle of
functional relativity is introduced which states that quantum theory is indeed
a functional tensor theory, i.e., it can be described by functional tensor
equations. The main equations of quantum theory are shown to be compatible with
the principle of functional relativity. By accepting the principle as a
hypothesis, we then analyze the origin of physical dimensions, provide a
geometric interpretation of Planck's constant, and find a simple interpretation
of the two-slit experiment and the process of measurement.Comment: 45 pages, 9 figures, see arXiv:0704.3225v1 for mathematical
considerations and http://www.uwc.edu/dept/math/faculty/kryukov/ for related
paper
On a different BRST constructions for a given Lie algebra
The method of the BRST quantization is considered for the system of
constraints, which form a Lie algebra. When some of the Cartan generators do
not imply any conditions on the physical states, the system contains the first
and the second class constraints. After the introduction auxiliary bosonic
degrees of freedom for these cases, the corresponding BRST charges with the
nontrivial structure of nonlinear terms in ghosts are constructed.Comment: 10 Pages, LaTe
Affine configurations and pure braids
We show that the fundamental group of the space of ordered affine-equivalent
configurations of at least five points in the real plane is isomorphic to the
pure braid group modulo its centre. In the case of four points this fundamental
group is free with eleven generators.Comment: 5 pages, 1 figure, final version; to appear in Discrete &
Computational Geometry, available from the publishers at
http://www.springerlink.com/content/384516n7q24811ph
Invariance in adelic quantum mechanics
Adelic quantum mechanics is form invariant under an interchange of real and
p-adic number fields as well as rings of p-adic integers. We also show that in
adelic quantum mechanics Feynman's path integrals for quadratic actions with
rational coefficients are invariant under changes of their entries within
nonzero rational numbers.Comment: 6 page
Singularities of bi-Hamiltonian systems
We study the relationship between singularities of bi-Hamiltonian systems and
algebraic properties of compatible Poisson brackets. As the main tool, we
introduce the notion of linearization of a Poisson pencil. From the algebraic
viewpoint, a linearized Poisson pencil can be understood as a Lie algebra with
a fixed 2-cocycle. In terms of such linearizations, we give a criterion for
non-degeneracy of singular points of bi-Hamiltonian systems and describe their
types
The transformation of irreducible tensor operators under spherical functions
The irreducible tensor operators and their tensor products employing Racah
algebra are studied. Transformation procedure of the coordinate system
operators act on are introduced. The rotation matrices and their
parametrization by the spherical coordinates of vector in the fixed and rotated
coordinate systems are determined. A new way of calculation of the irreducible
coupled tensor product matrix elements is suggested. As an example, the
proposed technique is applied for the matrix element construction for two
electrons in a field of a fixed nucleus.Comment: To appear in Int. J. Theor. Phy
Bosonic String and String Field Theory: a solution using Ultradistributions of Exponential Type
In this paper we show that Ultradistributions of Exponential Type (UET) are
appropriate for the description in a consistent way string and string field
theories. A new Lagrangian for the closed string is obtained and shown to be
equivalent to Nambu-Goto's Lagrangian. We also show that the string field is a
linear superposition of UET of compact support CUET). We evaluate the
propagator for the string field, and calculate the convolution of two of them.Comment: 30 page
Extensions of superalgebras of Krichever-Novikov type
An explicit construction of central extensions of Lie superalgebras of
Krichever-Novikov type is given. In the case of Jordan superalgebras related to
the superalgebras of Krichever-Novikov type we calculate a 1-cocycle with
coefficients in the dual space
Singular Tropical Hypersurfaces
We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal intersection points of planar tropical curves
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