219 research outputs found

### Dressed coordinates: the path-integrals approach

The recent introduced \textit{dressed coordinates} are studied in the
path-integral approach. These coordinates are defined in the context of a
harmonic oscillator linearly coupled to massless scalar field and, it is shown
that in this model the dressed coordinates appear as a coordinate
transformation preserving the path-integral functional measure. The analysis
also generalizes the \textit{sum rules} established in a previous work.Comment: 9 pages, Latex2

### A supersymmetric exotic field theory in (1+1) dimensions. One loop soliton quantum mass corrections

We consider one loop quantum corrections to soliton mass for the ${\cal N}=1$
supersymmetric extension of the (1+1)-dimensional scalar field theory with the
potential $U(\phi) = \phi^2 \cos^2\left(\ln \phi^2\right)$. First, we compute
the one loop quantum soliton mass correction of the bosonic sector. To do that,
we regularize implicitly such quantity by subtracting and adding its
corresponding tadpole graph contribution, and use the renormalization
prescription that the added term vanishes with the corresponding counterterms.
As a result we get a finite unambiguous formula for the soliton quantum mass
corrections up to one loop order. Afterwards, the computation for the
supersymmetric case is extended straightforwardly and we obtain for the one
loop quantum correction of the SUSY kink mass the expected value previously
derived for the SUSY sine-Gordon and $\phi^4$ models. However, we also have
found that for a particular value of the parameters, contrary to what was
expected, the introduction of supersymmetry in this model worsens ultraviolet
divergences rather than improving them.Comment: 16 pages, 8 figures; Major modifications included to match version
published in JHE

### Sum rules in the oscillator radiation processes

We consider the problem of an harmonic oscillator coupled to a scalar field
in the framework of recently introduced dressed coordinates. We compute all the
probabilities associated with the decay process of an excited level of the
oscillator. Instead of doing direct quantum mechanical calculations we
establish some sum rules from which we infer the probabilities associated to
the different decay processes of the oscillator. Thus, the sum rules allows to
show that the transition probabilities between excited levels follow a binomial
distribution.Comment: comments and references added, LaTe

### Renormalized coordinate approach to the thermalization process

We consider a particle in the harmonic approximation coupled linearly to an
environment. modeled by an infinite set of harmonic oscillators. The system
(particle--environment) is considered in a cavity at thermal equilibrium. We
employ the recently introduced notion of renormalized coordinates to
investigate the time evolution of the particle occupation number. For
comparison we first present this study in bare coordinates. For a long ellapsed
time, in both approaches, the occupation number of the particle becomes
independent of its initial value. The value of ocupation number of the particle
is the physically expected one at the given temperature. So we have a Markovian
process, describing the particle thermalization with the environment. With
renormalized coordinates no renormalization procedure is required, leading
directly to a finite result.Comment: 16 pages, LATEX, 2 figure

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