362 research outputs found
Lehmann-Symanzik-Zimmermann Reduction Approach to Multi-Photon Scattering in Coupled-Resonator Arrays
We present a quantum field theoretical approach based on the
Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process
in a nano-architecture consisting of the coupled resonator arrays (CRA), which
are also coupled to some artificial atoms as the controlling quantum node. By
making use of this approach, we find the bound states of single photon for an
elementary unit, the T-type CRA, and explicitly obtain its multi-photon
scattering S-matrix in various situations. We also use this method to calculate
the multi-photon S-matrices for the more complex quantum network constructed
with main T-type CRA's, such as a H-type CRA waveguide.Comment: 15 pages, 14 figure
Twisted supersymmetric 5D Yang-Mills theory and contact geometry
We extend the localization calculation of the 3D Chern-Simons partition
function over Seifert manifolds to an analogous calculation in five dimensions.
We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined
on a circle bundle over a four dimensional symplectic manifold. The notion of
contact geometry plays a crucial role in the construction and we suggest a
generalization of the instanton equations to five dimensional contact
manifolds. Our main result is a calculation of the full perturbative partition
function on a five sphere for the twisted supersymmetric Yang-Mills theory with
different Chern-Simons couplings. The final answer is given in terms of a
matrix model. Our construction admits generalizations to higher dimensional
contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov
from the mid 90's, and in a way it is covariantization of their ideas for a
contact manifold.Comment: 28 pages; v2: minor mistake corrected; v3: matches published versio
Ghost Busting: PT-Symmetric Interpretation of the Lee Model
The Lee model was introduced in the 1950s as an elementary quantum field
theory in which mass, wave function, and charge renormalization could be
carried out exactly. In early studies of this model it was found that there is
a critical value of g^2, the square of the renormalized coupling constant,
above which g_0^2, the square of the unrenormalized coupling constant, is
negative. Thus, for g^2 larger than this critical value, the Hamiltonian of the
Lee model becomes non-Hermitian. It was also discovered that in this
non-Hermitian regime a new state appears whose norm is negative. This state is
called a ghost state. It has always been assumed that in this ghost regime the
Lee model is an unacceptable quantum theory because unitarity appears to be
violated. However, in this regime while the Hamiltonian is not Hermitian, it
does possess PT symmetry. It has recently been discovered that a non-Hermitian
Hamiltonian having PT symmetry may define a quantum theory that is unitary. The
proof of unitarity requires the construction of a new time-independent operator
called C. In terms of C one can define a new inner product with respect to
which the norms of the states in the Hilbert space are positive. Furthermore,
it has been shown that time evolution in such a theory is unitary. In this
paper the C operator for the Lee model in the ghost regime is constructed
exactly in the V/N-theta sector. It is then shown that the ghost state has a
positive norm and that the Lee model is an acceptable unitary quantum field
theory for all values of g^2.Comment: 20 pages, 9 figure
New spectra in the HEIDI Higgs models
We study the so-called HEIDI models, which are renormalizable extensions of
the standard model with a higher dimensional scalar singlet field. As an
additional parameter we consider a higher-dimensional mixing mass parameter.
This leads to enriched possibilities compared to a previous study. We find
effective spectral densities of the Higgs propagator, consisting of one, two or
no particle peaks, together with a continuum. We compare with the LEP-2 data
and determine for which range of the model parameters the data can be
described. Assuming two peaks to be present we find for the new mass scale
\nu\approx 56\pm12 \gev, largely independent of the dimension. In the
limiting case of and two peaks we find a higher dimensional
coupling constant , indicative of strong interactions
among the higher dimensional fields. The LHC will not be able to study this
Higgs field.Comment: 17 pages, 4 figure
Revisiting soliton contributions to perturbative amplitudes
Open Access funded by SCOAP3. CP is
a Royal Society Research Fellow and partly supported by the U.S. Department of Energy
under grants DOE-SC0010008, DOE-ARRA-SC0003883 and DOE-DE-SC0007897. ABR
is supported by the Mitchell Family Foundation. We would like to thank the Mitchell
Institute at Texas A&M and the NHETC at Rutgers University respectively for hospitality
during the course of this work. We would also like to acknowledge the Aspen Center for
Physics and NSF grant 1066293 for a stimulating research environment
A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics
We study a mean-field relativistic model which is able to describe both the
behavior of finitely many spin-1/2 particles like electrons and of the Dirac
sea which is self-consistently polarized in the presence of the real particles.
The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the
photon field. All our results are non-perturbative and mathematically rigorous.Comment: 18 pages, 3 figure
Phases of planar 5-dimensional supersymmetric Chern-Simons theory
In this paper we investigate the large- behavior of 5-dimensional
super Yang-Mills with a level Chern-Simons term and an
adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must
choose an integration contour to completely define the theory. Using
localization, we reduce the path integral to a matrix model with a cubic action
and compute its free energy in various scenarios. In the limit of infinite
Yang-Mills coupling and for particular choices of the contours, we find that
the free-energy scales as for gauge groups with large values
of the Chern-Simons 't\,Hooft coupling, . If we also
set the hypermultiplet mass to zero, then this limit is a superconformal fixed
point and the behavior parallels other fixed points which have known
supergravity duals. We also demonstrate that gauge groups cannot have
this scaling for their free-energy. At finite Yang-Mills coupling we
establish the existence of a third order phase transition where the theory
crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase
transition exists for any value of , although the details differ
between small and large values of . For pure Chern-Simons
theories we present evidence for a chain of phase transitions as
is increased.
We also find the expectation values for supersymmetric circular Wilson loops
in these various scenarios and show that the Chern-Simons term leads to
different physical properties for fundamental and anti-fundamental Wilson
loops. Different choices of the integration contours also lead to different
properties for the loops.Comment: 40 pages, 17 figures, Minor corrections, Published versio
The running of the electromagnetic coupling alpha in small-angle Bhabha scattering
A method to determine the running of alpha from a measurement of small-angle
Bhabha scattering is proposed and worked out. The method is suited to high
statistics experiments at e+e- colliders, which are equipped with luminometers
in the appropriate angular region. A new simulation code predicting small-angle
Bhabha scattering is also presentedComment: 15 pages, 3 Postscript figure
Improved Term of the Electron Anomalous Magnetic Moment
We report a new value of electron , or , from 891 Feynman diagrams
of order . The FORTRAN codes of 373 diagrams containing closed
electron loops have been verified by at least two independent formulations. For
the remaining 518 diagrams, which have no closed lepton loop, verification by a
second formulation is not yet attempted because of the enormous amount of
additional work required. However, these integrals have structures that allow
extensive cross-checking as well as detailed comparison with lower-order
diagrams through the renormalization procedure. No algebraic error has been
uncovered for them. The numerical evaluation of the entire term by
the integration routine VEGAS gives , where the
uncertainty is obtained by careful examination of error estimates by VEGAS.
This leads to ,
where the uncertainties come from the term, the estimated
uncertainty of term, and the inverse fine structure constant,
, measured by atom interferometry combined
with a frequency comb technique, respectively. The inverse fine structure
constant derived from the theory and the Seattle
measurement of is .Comment: 64 pages and 10 figures. Eq.(16) is corrected. Comments are added
after Eq.(40
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