60 research outputs found
Obtaining the Gauge Invariant Kinetic Term for a SU(n) x SU(m) Lagrangian
We propose a generalized way to formally obtain the gauge invariance of the
kinetic part of a field Lagrangian over which a gauge transformation ruled by
an coupling symmetry is applied. As an
illustrative example, we employ such a formal construction for reproducing the
standard model Lagrangian. This generalized formulation is supposed to
contribute for initiating the study of gauge transformation applied to
generalized symmetries as well as for
complementing an introductory study of the standard model of elementary
particles.Comment: 6 page
Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?
We make a comparison between results from numerically generated,
quasi-equilibrium configurations of compact binary systems of black holes in
close orbits, and results from the post-Newtonian approximation. The
post-Newtonian results are accurate through third PN order (O(v/c)^6 beyond
Newtonian gravity), and include rotational and spin-orbit effects, but are
generalized to permit orbits of non-zero eccentricity. Both treatments ignore
gravitational radiation reaction. The energy E and angular momentum J of a
given configuration are compared between the two methods as a function of the
orbital angular frequency \Omega. For small \Omega, corresponding to orbital
separations a factor of two larger than that of the innermost stable orbit, we
find that, if the orbit is permitted to be slightly eccentric, with e ranging
from \approx 0.03 to \approx 0.05, and with the two objects initially located
at the orbital apocenter (maximum separation), our PN formulae give much better
fits to the numerically generated data than do any circular-orbit PN methods,
including various ``effective one-body'' resummation techniques. We speculate
that the approximations made in solving the initial value equations of general
relativity numerically may introduce a spurious eccentricity into the orbits.Comment: 6 pages, 4 figures, to be submitted to Phys. Rev.
Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
An equation of motion for relativistic compact binaries is derived through
the third post-Newtonian (3 PN) approximation of general relativity. The strong
field point particle limit and multipole expansion of the stars are used to
solve iteratively the harmonically relaxed Einstein equations. We take into
account the Lorentz contraction on the multipole moments defined in our
previous works. We then derive a 3 PN acceleration of the binary orbital motion
of the two spherical compact stars based on a surface integral approach which
is a direct consequence of local energy momentum conservation. Our resulting
equation of motion admits a conserved energy (neglecting the 2.5 PN radiation
reaction effect), is Lorentz invariant and is unambiguous: there exist no
undetermined parameter reported in the previous works. We shall show that our 3
PN equation of motion agrees physically with the Blanchet and Faye 3 PN
equation of motion if , where is the parameter
which is undetermined within their framework. This value of is
consistent with the result of Damour, Jaranowski, and Sch\"afer who first
completed a 3 PN iteration of the ADM Hamiltonian in the ADMTT gauge using the
dimensional regularization.Comment: 52 pages, no figure, Appendices B and D added. Phys. Rev. D in pres
Transition from band insulator to Mott insulator in one dimension: Critical behavior and phase diagram
We report a systematic study of the transition from a band insulator (BI) to
a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with
an on-site Coulomb interaction U and an alternating periodic site potential V.
We employ both the zero-temperature density matrix renormalization group (DMRG)
method to determine the gap and critical behavior of the system and the
finite-temperature transfer matrix renormalization group method to evaluate the
thermodynamic properties. We find two critical points at U = and U =
that separate the BI and MI phases for a given V. A charge-neutral
spin-singlet exciton band develops in the BI phase (U<) and drops below
the band gap when U exceeds a special point Ue. The exciton gap closes at the
first critical point while the charge and spin gaps persist and coincide
between <U< where the system is dimerized. Both the charge and spin
gaps collapse at U = when the transition to the MI phase occurs. In the
MI phase (U>) the charge gap increases almost linearly with U while the
spin gap remains zero. These findings clarify earlier published results on the
same model, and offer insights into several important issues regarding an
appropriate scaling analysis of DMRG data and a full physical picture of the
delicate nature of the phase transitions driven by electron correlation. The
present work provides a comprehensive understanding for the critical behavior
and phase diagram for the transition from BI to MI in one-dimensional
correlated electron systems with a periodic alternating site potential.Comment: long version, 10 figure
On the Circular Orbit Approximation for Binary Compact Objects In General Relativity
One often-used approximation in the study of binary compact objects (i.e.,
black holes and neutron stars) in general relativity is the instantaneously
circular orbit assumption. This approximation has been used extensively, from
the calculation of innermost circular orbits to the construction of initial
data for numerical relativity calculations. While this assumption is
inconsistent with generic general relativistic astrophysical inspiral phenomena
where the dissipative effects of gravitational radiation cause the separation
of the compact objects to decrease in time, it is usually argued that the
timescale of this dissipation is much longer than the orbital timescale so that
the approximation of circular orbits is valid. Here, we quantitatively analyze
this approximation using a post-Newtonian approach that includes terms up to
order ({Gm/(rc^2)})^{9/2} for non-spinning particles. By calculating the
evolution of equal mass black hole / black hole binary systems starting with
circular orbit configurations and comparing them to the more astrophysically
relevant quasicircular solutions, we show that a minimum initial separation
corresponding to at least 6 (3.5) orbits before plunge is required in order to
bound the detection event loss rate in gravitational wave detectors to < 5%
(20%). In addition, we show that the detection event loss rate is > 95% for a
range of initial separations that include all modern calculations of the
innermost circular orbit (ICO).Comment: 10 pages, 12 figures, revtex
Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model
We revisit the ground-state phase diagram of the one-dimensional half-filled
extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive
interactions. In the first half of the paper, using the weak-coupling
renormalization-group approach (g-ology) including second-order corrections to
the coupling constants, we show that bond-charge-density-wave (BCDW) phase
exists for U \approx 2V in between charge-density-wave (CDW) and
spin-density-wave (SDW) phases. We find that the umklapp scattering of
parallel-spin electrons disfavors the BCDW state and leads to a bicritical
point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into
the CDW-SDW first-order transition line. In the second half of the paper, we
investigate the phase diagram of the extended Hubbard model with either
additional staggered site potential \Delta or bond alternation \delta. Although
the alternating site potential \Delta strongly favors the CDW state (that is, a
band insulator), the BCDW state is not destroyed completely and occupies a
finite region in the phase diagram. Our result is a natural generalization of
the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014
(1999)], who predicted the existence of a spontaneously dimerized insulating
state between a band insulator and a Mott insulator in the phase diagram of the
ionic Hubbard model. The bond alternation \delta destroys the SDW state and
changes it into the BCDW state (or Peierls insulating state). As a result the
phase diagram of the model with \delta contains only a single critical line
separating the Peierls insulator phase and the CDW phase. The addition of
\Delta or \delta changes the universality class of the CDW-BCDW transition from
the Gaussian transition into the Ising transition.Comment: 24 pages, 20 figures, published versio
Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
Dimensional regularization is used to derive the equations of motion of two
point masses in harmonic coordinates. At the third post-Newtonian (3PN)
approximation, it is found that the dimensionally regularized equations of
motion contain a pole part [proportional to 1/(d-3)] which diverges as the
space dimension d tends to 3. It is proven that the pole part can be
renormalized away by introducing suitable shifts of the two world-lines
representing the point masses, and that the same shifts renormalize away the
pole part of the "bulk" metric tensor g_munu(x). The ensuing, finite
renormalized equations of motion are then found to belong to the general
parametric equations of motion derived by an extended Hadamard regularization
method, and to uniquely determine the heretofore unknown 3PN parameter lambda
to be: lambda = - 1987/3080. This value is fully consistent with the recent
determination of the equivalent 3PN static ambiguity parameter, omega_s = 0, by
a dimensional-regularization derivation of the Hamiltonian in
Arnowitt-Deser-Misner coordinates. Our work provides a new, powerful check of
the consistency of the dimensional regularization method within the context of
the classical gravitational interaction of point particles.Comment: 82 pages, LaTeX 2e, REVTeX 4, 8 PostScript figures, minor changes to
reflect Phys. Rev. D versio
An Extended Technicolor Model With QCD-like Symmetry Breaking
We present a one-doublet extended technicolor model, with all fermions in
fundamental representations. The bare lagrangian has no explicit mass terms but
generates masses through gauge symmetry breaking by purely QCD-like dynamics.
The model generates three families of quarks and leptons and can accommodate
the observed third family mass spectrum (including a large top mass and light
neutrinos). In addition, we show how the model may be extended to incorporate a
top color driven top mass without the need for a strong U(1) interaction. We
discuss the compatiblity of the model with experimental constraints and its
possible predicitive power with respect to first and second family masses.Comment: 25 pages, latex, 7 figure
Yukawa coupling unification and non-universal gaugino mediation of supersymmetry breaking
The requirement of Yukawa coupling unification highly constrains the SUSY
parameter space. In several SUSY breaking scenarios it is hard to reconcile
Yukawa coupling unification with experimental constraints from B(b->s gamma)
and the muon anomalous magnetic moment a_mu. We show that b-tau or even t-b-tau
Yukawa unification can be satisfied simultaneously with b->s gamma and a_mu in
the non-universal gaugino mediation scenario. Non-universal gaugino masses
naturally appear in higher dimensional grand unified models in which gauge
symmetry is broken by orbifold compactification. Relations between SUSY
contributions to fermion masses, b->s gamma and a_mu which are typical for
models with universal gaugino masses are relaxed. Consequently, these
phenomenological constraints can be satisfied simultaneously with a relatively
light SUSY spectrum, compared to models with universal gaugino masses.Comment: 20 pages, 8 figures. References added. A copy of the paper with
better resolution figures can be found at
http://www.hep.fsu.edu/~balazs/Physics/Papers/2003
The Weak Charge of the Proton and New Physics
We address the physics implications of a precision determination of the weak
charge of the proton, QWP, from a parity violating elastic electron proton
scattering experiment to be performed at the Jefferson Laboratory. We present
the Standard Model (SM) expression for QWP including one-loop radiative
corrections, and discuss in detail the theoretical uncertainties and missing
higher order QCD corrections. Owing to a fortuitous cancellation, the value of
QWP is suppressed in the SM, making it a unique place to look for physics
beyond the SM. Examples include extra neutral gauge bosons, supersymmetry, and
leptoquarks. We argue that a QWP measurement will provide an important
complement to both high energy collider experiments and other low energy
electroweak measurements. The anticipated experimental precision requires the
knowledge of the order alpha_s corrections to the pure electroweak box
contributions. We compute these contributions for QWP, as well as for the weak
charges of heavy elements as determined from atomic parity violation.Comment: 22 pages of LaTeX, 5 figure
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