# I need hep-th/9312153

1. Sep 8, 2009

### luxxio

but arxiv.org tell me that the pdf (or ps) is not available. the latex format don't work. someone can tell me where i can found it? thanx

2. Sep 8, 2009

### marcus

I hope someone else can help. I would write email to one of the authors.
This is what happened to me when I tried. I went to the abstract and clicked on PDF.
I got an error message which said that they have the source but they cannot convert to PDF and it tells me to write email to the authors.

But the word "source" is a link. So I click on that and I get what looks like a text file for the paper itself. I can read, or almost read, this text file. The abstract and the list of references to other papers come first. Then I scroll down and get to the main body of the paper, which looks like this (this is just a short sample):

==quote==
Recently, many proposals were presented showing how to apply the ideas of
quantum deformations [\rone-\rthree] to the $D=4$ Poincar\'e algebra
[\rfour-\rten] as well as
the $D=4$ Poincar\'e group [\releven-\rsixteen].
The $\kappa$-deformation of the $D=4$ Poincar\'e algebra, first proposed
in [\rfour,\reight], leads to the modification of relativistic symmetries with
the
three-dimensional $E(3)$ subalgebra unchanged. The deformation
parameter $\kappa$ describes the fundamental mass in the theory
and the limit $\kappa\rightarrow \infty$ corresponds to the undeformed case.

As a consequence of the \k deformation the mass shell condition is changed as
follows ( $\vec p\sp2\equiv p_1\sp2+p_2\sp2+p_3\sp2$) [\reight]:

$$p_0\sp2- \vec p\sp2=m\sp2\quad\rightarrow\quad \bigl(2\kappa sinh{p_0\over 2\kappa}\bigr)\sp2-\vec p\sp2=m\sp2.\eqn\eonethree$$
The \k-deformed mass-shell condition leads to the following modification of
the Hamiltonian of free
\k-relativistic particles:
$$H=P_0=\sqrt{\vec P\sp2+M\sp2}\; \rightarrow\;H_0\sp{\kappa}=P_0=2\kappa\,arcsinh{\sqrt{\vec P\sp2+M\sp2}\over 2\kappa}.\eqn\eonetwo$$

In the \k-deformed Poincar\'e algebra, which we describe in section 2,
the four-momenta commute and
we can introduce the space-time
dependence by
the standard Fourier transforms of the four-momenta functions. In such a way we
can choose
the \k-relativistic classical mechanics
to be formulated in terms of
space coordinates satisfying standard relativistic Poisson brackets:
$$\{x\sp{\mu},p\sp{\nu}\}=i\eta\sp{\mu\nu},\qquad \hbox{diag}\eta=(-1,1,1,1). \eqn\eonefour$$
The form of the Hamilton equations of motion remains also unchanged \ie\
we have
$$\dot x_i={\partial H\sp{\kappa}\over \partial p_i},\quad \dot p_i=-{\partial H\sp{\kappa}\over \partial x_i}.\eqn\eonefive$$
In such an approach the only change due to the \k-deformation
is the explicit form of the
Hamiltonian (see \eonetwo\ for the free case).

In section 3 we present the Hamiltonian and Lagrangian formalism
for both the massive and massless
free \k-relativistic particles described by the Hamiltonian
$H_0\sp{\kappa}$.
As is known [\rseventeen,\reighteen,\rten], however, the velocity decreases
with the increase
of energy at large
energies ($E\gg \kappa m$) in such a model.

To eliminate the velocity decrease with the increase of energy
we present in section 4 two
possible remedies:
\item{i)} The introduction of space coordinates with nonvanishing Poisson
brackets.
We consider massive spinless systems and we
introduce the three space coordinates $x\sp{i}$ as the
functions of the \k deformed Poincar\'e algebra generators.
The standard choice, with space variables satisfying \eonefour\ (for
$\mu,\nu=1,2,3$) was found by
Bacry [\reighteen, \rten]. Recently Maggiore [\rnineteen]
proposed other functions
of the \k Poincar\'e generators
which even for a spinless system describe space coordinates with
nonvanishing Poisson brackets. It appears that such a proposal fits nicely
into the schemes in which the symplectic tensor determining
the Hamilton equations is not canonical.
...
...
==endquote==

3. Sep 8, 2009

### xepma

Last edited by a moderator: May 4, 2017
4. Sep 8, 2009

### luxxio

Last edited by a moderator: May 4, 2017
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