2,178 research outputs found

### Monopoles, Duality, and String Theory

Dirac showed that the existence of magnetic monopoles would imply
quantization of electric charge. I discuss the converse, and propose two
`principles of completeness' which I illustrate with various examples.Comment: Presented at the Dirac Centennial Symposium, Tallahassee, Dec. 6-7,
200

### A Field Theory Model With a New Lorentz-Invariant Energy Scale

A framework is proposed that allows to write down field theories with a new
energy scale while explicitly preserving Lorentz invariance and without
spoiling the features of standard quantum field theory which allow quick
calculations of scattering amplitudes. If the invariant energy is set to the
Planck scale, these deformed field theories could serve to model quantum
gravity phenomenology. The proposal is based on the idea, appearing for example
in Deformed Special Relativity, that momentum space could be curved rather than
flat. This idea is implemented by introducing a fifth dimension and imposing an
extra constraint on physical field configurations in addition to the mass shell
constraint. It is shown that a deformed interacting scalar field theory is
unitary. Also, a deformed version of QED is argued to give scattering
amplitudes that reproduce the usual ones in the leading order. Possibilities
for experimental signatures are discussed, but more work on the framework's
consistency and interpretation is necessary to make concrete predictions.Comment: 20 page

### Dominant $2\pi\gamma$-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials

We calculate at two-loop order in chiral perturbation theory the
electromagnetic corrections to the two-pion exchange nucleon-nucleon
interaction that is generated by the isovector spin-flip $\pi\pi NN$
contact-vertex proportional to the large low-energy constant $c_4\simeq 3.4$GeV$^{-1}$. We find that the respective $2\pi\gamma$-exchange potentials
contain sizeable isospin-breaking components which reach up to -4% of
corresponding isovector $2\pi$-exchange potentials. The typical values of these
novel charge-independence breaking spin-spin and tensor potentials are $-0.11$MeV and $0.09$MeV, at a nucleon distance of $r=m_\pi^{-1}=1.4$fm. The
charge-symmetry breaking spin-spin and tensor potentials come out a factor of
2.4 smaller. Our analytical results for these presumably dominant
isospin-violating spin-spin and tensor NN-forces are in a form such that they
can be easily implemented into phase-shift analyses and few-body calculations.Comment: 7 pages, 1 figure, 2 tables, to be published in Physical Review C:
Brief report

### Vacuum Stability of the $\mathcal{PT}$-Symmetric $\left( -\phi^{4}\right)$ Scalar Field Theory

In this work, we study the vacuum stability of the classical unstable $\left(
-\phi^{4}\right)$ scalar field potential. Regarding this, we obtained the
effective potential, up to second order in the coupling, for the theory in
$1+1$ and $2+1$ space-time dimensions. We found that the obtained effective
potential is bounded from below, which proves the vacuum stability of the
theory in space-time dimensions higher than the previously studied $0+1$ case.
In our calculations, we used the canonical quantization regime in which one
deals with operators rather than classical functions used in the path integral
formulation. Therefore, the non-Hermiticity of the effective field theory is
obvious. Moreover, the method we employ implements the canonical equal-time
commutation relations and the Heisenberg picture for the operators. Thus, the
metric operator is implemented in the calculations of the transition
amplitudes. Accordingly, the method avoids the very complicated calculations
needed in other methods for the metric operator. To test the accuracy of our
results, we obtained the exponential behavior of the vacuum condensate for
small coupling values, which has been obtained in the literature using other
methods. We assert that this work is interesting, as all the studies in the
literature advocate the stability of the $\left( -\phi^{4}\right)$ theory at
the quantum mechanical level while our work extends the argument to the level
of field quantization.Comment: 20 pages, 4 figures, appendix added and more details have been added
to

### Electromagnetic corrections to the dominant two-pion exchange nucleon-nucleon potential

We calculate at two-loop order in chiral perturbation theory the
electromagnetic corrections to the dominant two-pion exchange nucleon-nucleon
interaction that is generated by the isoscalar $\pi N$ contact-vertex
proportional to the large low-energy constant $c_3$. We find that the
respective $2\pi\gamma$-exchange potential contains sizeable isospin-breaking
components which amount to about -1% of the strongly attractive isoscalar
central $2\pi$-exchange potential. The typical value of these novel
charge-independence and charge-symmetry breaking central potentials is $0.3$MeV at a nucleon distance of $r= m_\pi^{-1} = 1.4$fm. Our analytical result
for this presumably dominant $2\pi\gamma$-exchange interaction is in a form
such that it can be easily implemented into phase-shift analyses and few-body
calculations.Comment: 7 pages, 1 figure, to be published in Physical Review C (2006): Brief
Report

### About flavor, spin and color

Chiral symmetry breaking (restoration) for SU(N) gauge theories is a topic of
great interest and not yet fully explained. We consider the phenomenon as a
collective spin effect and determine its behavior in terms of the number of
flavors, N_f.Comment: version to be published in Phys. Rev.

### Effective Field calculations of the Energy Spectrum of the $\mathcal{PT}%$-Symmetric ($-x^{4}$) Potential

In this work, we show that the traditional effective field approach can be
applied to the $\mathcal{PT}$-symmetric wrong sign ($-x^{4}$) quartic
potential. The importance of this work lies in the possibility of its extension
to the more important $\mathcal{PT}$-symmetric quantum field theory while the
other approaches which use complex contours are not willing to be applicable.
We calculated the effective potential of the massless $-x^{4}$ theory as well
as the full spectrum of the theory. Although the calculations are carried out
up to first order in the coupling, the predicted spectrum is very close to the
exact one taken from other works. The most important result of this work is
that the effective potential obtained, which is equivalent to the Gaussian
effective potential, is bounded from below while the classical potential is
bounded from above. This explains the stability of the vacuum of the theory.
The obtained quasi-particle Hamiltonian is non-Hermitian but
$\mathcal{PT}$-symmetric and we showed that the calculation of the metric
operator can go perturbatively. In fact, the calculation of the metric operator
can be done even for higher dimensions (quantum field theory) which, up till
now, can not be calculated in the other approaches either perturbatively or in
a closed form due to the possible appearance of field radicals. Moreover, we
argued that the effective theory is perturbative for the whole range of the
coupling constant and the perturbation series is expected to converge rapidly
(the effective coupling $g_{eff}={1/6}$).Comment: 14 pages, 5 figure

### Thermal Field Theory in a wire: Applications of Thermal Field Theory methods to the propagation of photons in a one-dimensional plasma

We apply the Thermal Field Theory (TFT) methods to study the propagation of
photons in a plasma wire, that is, a system in which the electrons are confined
to a one-dimensional tube or wire, but are otherwise free. We find the
appropriate expression for the photon \emph{free-field} propagator in such a
medium, and write down the dispersion relation in terms of the free-field
propagator and the photon self-energy. The self-energy is then calculated in
the one-loop approximation and the corresponding dispersion relation is
determined and studied in some detail. Our work differs from previous work on
this subject in that we do not adopt any specific electronic wave functions in
the coordinates that are transverse to the idealized wire, or rely on
particular features of the electronic structure. We treat the electrons as a
free gas of particles, constrained to move in one dimension, but otherwise in a
model-independent way only following the rules of TFT adapted to the situation
at hand. For the appropriate conditions of the plasma the \emph{static
approximation} can be employed and the dispersion relation reduces to the
results obtained in previous works, but the formula that we obtain is valid
under more general conditions, including those in which the static
approximation is not valid. In particular, the dispersion relation has several
branches, which are not revealed if the static approximation is used. The
dispersion relations obtained reproduce several unique features of these
systems that have been observed in recent experiments.Comment: 17 pages Revised and extended discussion of the dispersion relation

### Theory of quasiparticle interference on the surface of a strong topological insulator

Electrons on the surface of a strong topological insulator, such as Bi2Te3 or
Bi1-xSnx, form a topologically protected helical liquid whose excitation
spectrum contains an odd number of massless Dirac fermions. A theoretical
survey and classification is given of the universal features, observable by the
ordinary and spin-polarized scanning tunneling spectroscopy, in the
interference patterns resulting from the quasiparticle scattering by magnetic
and non-magnetic impurities in such a helical liquid. Our results confirm the
absence of backscattering from non-magnetic impurities observed in recent
experiments and predict new interference features, uniquely characteristic of
the helical liquid, when the scatterers are magnetic.Comment: 4 pages, 2 figures, 1 table. Version to appear in PRB/RC; Typos
correcte

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