659 research outputs found
Quantum Thetas on Noncommutative T^4 from Embeddings into Lattice
In this paper we investigate the theta vector and quantum theta function over
noncommutative T^4 from the embedding of R x Z^2. Manin has constructed the
quantum theta functions from the lattice embedding into vector space (x finite
group). We extend Manin's construction of the quantum theta function to the
embedding of vector space x lattice case. We find that the holomorphic theta
vector exists only over the vector space part of the embedding, and over the
lattice part we can only impose the condition for Schwartz function. The
quantum theta function built on this partial theta vector satisfies the
requirement of the quantum theta function. However, two subsequent quantum
translations from the embedding into the lattice part are non-additive,
contrary to the additivity of those from the vector space part.Comment: 20 pages, LaTeX, version to appear in J. Phys.
Field Theory on Quantum Plane
We build the defomation of plane on a product of two copies of
algebras of functions on the plane. This algebra constains a subalgebra of
functions on the plane. We present general scheme (which could be used as well
to construct quaternion from pairs of complex numbers) and we use it to derive
differential structures, metric and discuss sample field theoretical models.Comment: LaTeX, 10 page
SUSY structures, representations and Peter-Weyl theorem for
The real compact supergroup is analized from different perspectives
and its representation theory is studied. We prove it is the only (up to
isomorphism) supergroup, which is a real form of
with reduced Lie group , and a link with SUSY structures on is established. We describe a large family of complex semisimple
representations of and we show that any -representation
whose weights are all nonzero is a direct sum of members of our family. We also
compute the matrix elements of the members of this family and we give a proof
of the Peter-Weyl theorem for
F-manifolds and geometry of information
The theory of -manifolds, and more generally, manifolds endowed with
commutative and associative multiplication of their tangent fields, was
discovered and formalised in various models of quantum field theory involving
algebraic and analytic geometry, at least since 1990's.
The focus of this paper consists in the demonstration that various spaces of
probability distributions defined and studied at least since 1960's also carry
natural structures of -manifolds.
This fact remained somewhat hidden in various domains of the vast territory
of models of information storing and transmission that are briefly surveyed
here
Killing spinors are Killing vector fields in Riemannian Supergeometry
A supermanifold M is canonically associated to any pseudo Riemannian spin
manifold (M_0,g_0). Extending the metric g_0 to a field g of bilinear forms
g(p) on T_p M, p\in M_0, the pseudo Riemannian supergeometry of (M,g) is
formulated as G-structure on M, where G is a supergroup with even part G_0\cong
Spin(k,l); (k,l) the signature of (M_0,g_0). Killing vector fields on (M,g)
are, by definition, infinitesimal automorphisms of this G-structure. For every
spinor field s there exists a corresponding odd vector field X_s on M. Our main
result is that X_s is a Killing vector field on (M,g) if and only if s is a
twistor spinor. In particular, any Killing spinor s defines a Killing vector
field X_s.Comment: 14 pages, latex, one typo correcte
On SUSY curves
In this note we give a summary of some elementary results in the theory of
super Riemann surfaces (SUSY curves)
On Macroscopic Energy Gap for -Quantum Mechanical Systems
The q-deformed harmonic oscillator within the framework of the recently
introduced Schwenk-Wess -Heisenberg algebra is considered. It is shown, that
for "physical" values , the gap between the energy levels decreases
with growing energy. Comparing with the other (real) -deformations of the
harmonic oscillator, where the gap instead increases, indicates that the
formation of the macroscopic energy gap in the Schwenk-Wess -Quantum
Mechanics may be avoided.Comment: 6 pages, TeX, PRA-HEP-92/1
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