63 research outputs found
Lie antialgebras: cohomology and representations
We describe the main algebraic and geometric properties of the class of
algebras introduced in [arXiv:0705.1629]. We discuss their origins in
symplectic geometry and associative algebra, and the notions of cohomology and
representations. We formulate classification theorems and give a number of
examples.Comment: 11 pages, XXVII Workshop, Geometrical Methods in Mathematical
Physics., Bialowieza : Pologne (2008
Lorentz Covariant Distributions with the Spectral Conditions
The Lorentz covariant tempered disributions with the supports in the product
of the closed upper light cones are described.Comment: 13 page
Topological spectrum of classical configurations
For any classical field configuration or mechanical system with a finite
number of degrees of freedom we introduce the concept of topological spectrum.
It is based upon the assumption that for any classical configuration there
exists a principle fiber bundle that contains all the physical and geometric
information of the configuration. The topological spectrum follows from the
investigation of the corresponding topological invariants. Examples are given
which illustrate the procedure and the significance of the topological spectrum
as a discretization relationship among the parameters that determine the
physical meaning of classical configurations
Time Asymmetric Quantum Mechanics
The meaning of time asymmetry in quantum physics is discussed. On the basis
of a mathematical theorem, the Stone--von Neumann theorem, the solutions of the
dynamical equations, the Schr\"odinger equation (1) for states or the
Heisenberg equation (6a) for observables are given by a unitary group. Dirac
kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions;
for this kind of RHS a mathematical theorem also leads to time symmetric group
evolution. Scattering theory suggests to distinguish mathematically between
states (defined by a preparation apparatus) and observables (defined by a
registration apparatus (detector)). If one requires that scattering resonances
of width and exponentially decaying states of lifetime
should be the same physical entities (for which
there is sufficient evidence) one is led to a pair of RHS's of Hardy functions
and connected with it, to a semigroup time evolution , with
the puzzling result that there is a quantum mechanical beginning of time, just
like the big bang time for the universe, when it was a quantum system. The
decay of quasi-stable particles is used to illustrate this quantum mechanical
time asymmetry. From the analysis of these processes, we show that the
properties of rigged Hilbert spaces of Hardy functions are suitable for a
formulation of time asymmetry in quantum mechanics
The Jacobi group and the squeezed states - some comments
The generalized coherent states attached to the Jacobi group realize the
squeezed states. Imposing hermitian conjugacy to the generators of the Jacobi
algebra, we find out the form of the weight function appearing in the scalar
product. We show effectively the orthonormality of the base functions with
respect to the scalar product. From the explicit form of the reproducing
kernel, we find out the expression of the multiplier in a holomorphic
representation of the Jacobi group.Comment: 9 pages, to appear in AIP Conference Proceedings, Geometric Methods
In Physics, Bialowieza (Poland), June 28 -July 4 2008, Editor(s): P.
Kielanowski, S. T. Ali, A. Odzijewicz, M. Schlichenmaier, Th. Vorono
Relativistic Equations for Spin Particles: What Can We Learn From Noncommutativity?
We derive relativistic equations for charged and neutral spin particles. The
approach for higher-spin particles is based on generalizations of the
Bargmann-Wigner formalism. Next, we study, what new physical information can
the introduction of non-commutativity give us. Additional non-commutative
parameters can provide a suitable basis for explanation of the origin of mass.Comment: 5 pages, aipproc.cls, no figures, presented at the XXVIII WGMP09,
Bialowieza, Poland, June 28-July 4, 2009. The extended version is contributed
to the 12th International Workshop "What Comes Beyond the Standard Models?",
July 14- 24, 2009, Bled, Sloveni
Noncommutative complex Grosse-Wulkenhaar model
This paper stands for an application of the noncommutative (NC) Noether
theorem, given in our previous work [AIP Proc 956 (2007) 55-60], for the NC
complex Grosse-Wulkenhaar model. It provides with an extension of a recent work
[Physics Letters B 653 (2007) 343-345]. The local conservation of
energy-momentum tensors (EMTs) is recovered using improvement procedures based
on Moyal algebraic techniques. Broken dilatation symmetry is discussed. NC
gauge currents are also explicitly computed.Comment: 8 page
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