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 2πγ2\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 PT\mathcal{PT}-Symmetric (−ϕ4)\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 PT\mathcal{PT}% -Symmetric (−x4-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