484 research outputs found
Exact solutions of Dirac equation on a 2D gravitational background
We obtain classes of two dimensional static Lorentzian manifolds, which
through the supersymmetric formalism of quantum mechanics admit the exact
solvability of Dirac equation on these curved backgrounds. Specially in the
case of a modified supersymmetric harmonic oscillator the wave function and
energy spectrum of Dirac equation is given explicitly.Comment: 10 pages, title changed, content reduced, some references removed, To
be published in PL
Equivalence of model space techniques and the renormalization group for a separable model problem
Lee-Suzuki similarity transformations and Krencigowa-Kuo folded diagrams are
two common methods used to derive energy independent model space effective
interactions for nuclear many-body systems. We demonstrate that these methods
are equivalent to a Renormalization Group (RG) analysis of a separable
potential model. The effective low-momentum potentials V_{eff} are shown to
give the same scaling equation that RG arguments predict. We find the new
result that the different model space techniques considered in this paper yield
a unique low-momentum V_{eff} when applied to the toy model problem.Comment: 10 pages. Minor content and stylistic change
Model-independent low momentum nucleon interaction from phase shift equivalence
We present detailed results for the model-independent low momentum
nucleon-nucleon interaction V_{low k}. By introducing a cutoff in momentum
space, we separate the Hilbert space into a low momentum and a high momentum
part. The renormalization group is used to construct the effective interaction
V_{low k} in the low momentum space, starting from various high precision
potential models commonly used in nuclear many-body calculations. With a cutoff
in the range of , the new potential V_{low k} is
independent of the input model, and reproduces the experimental phase shift
data for corresponding laboratory energies below , as well
as the deuteron binding energy with similar accuracy as the realistic input
potentials. The model independence of V_{low k} demonstrates that the physics
of nucleons interacting at low momenta does not depend on details of the high
momentum dynamics assumed in conventional potential models. V_{low k} does not
have momentum components larger than the cutoff, and as a consequence is
considerably softer than the high precision potentials. Therefore, when V_{low
k} is used as microscopic input in the many-body problem, the high momentum
effects in the particle-particle channel do not have to be addressed by
performing a Brueckner ladder resummation or short-range correlation methods.
By varying the cutoff, we study how the model independence of V_{low k} is
reached in different partial waves. This provides numerical evidence for the
separation of scales in the nuclear problem, and physical insight into the
nature of the low momentum interaction.Comment: 32 pages, 19 figure
Convergence of the Born Series with Low-Momentum Interactions
The nonperturbative nature of nucleon-nucleon interactions as a function of a
momentum cutoff is studied using Weinberg eigenvalues as a diagnostic. This
investigation extends an earlier study of the perturbative convergence of the
Born series to partial waves beyond the 3S1-3D1 channel and to positive
energies. As the cutoff is lowered using renormalization-group or model-space
techniques, the evolution of nonperturbative features at large cutoffs from
strong short-range repulsion and the iterated tensor interaction are monitored
via the complex Weinberg eigenvalues. When all eigenvalues lie within the unit
circle, the expansion of the scattering amplitude in terms of the interaction
is perturbative, with the magnitude of the largest eigenvalue setting the rate
of convergence. Major decreases in the magnitudes of repulsive eigenvalues are
observed as the Argonne v18, CD-Bonn or Nijmegen potentials are evolved to low
momentum, even though two-body observables are unchanged. For chiral EFT
potentials, running the cutoff lower tames the impact of the tensor force and
of new nonperturbative features entering at N3LO. The efficacy of separable
approximations to nuclear interactions derived from the Weinberg analysis is
studied as a function of cutoff, and the connection to inverse scattering is
demonstrated.Comment: 21 pages, 15 figures, minor additions, to appear in Nucl. Phys.
Weinberg Eigenvalues and Pairing with Low-Momentum Potentials
The nonperturbative nature of nucleon-nucleon interactions evolved to low
momentum has recently been investigated in free space and at finite density
using Weinberg eigenvalues as a diagnostic. This analysis is extended here to
the in-medium eigenvalues near the Fermi surface to study pairing. For a fixed
value of density and cutoff Lambda, the eigenvalues increase arbitrarily in
magnitude close to the Fermi surface, signaling the pairing instability. When
using normal-phase propagators, the Weinberg analysis with complex energies
becomes a form of stability analysis and the pairing gap can be estimated from
the largest attractive eigenvalue. With Nambu-Gorkov Green's functions, the
largest attractive eigenvalue goes to unity close to the Fermi surface,
indicating the presence of bound states (Cooper pairs), and the corresponding
eigenvector leads to the self-consistent gap function.Comment: 16 pages, 9 figure
Is nuclear matter perturbative with low-momentum interactions?
The nonperturbative nature of inter-nucleon interactions is explored by
varying the momentum cutoff of a two-nucleon potential. Conventional force
models, which have large cutoffs, are nonperturbative because of strong
short-range repulsion, the iterated tensor interaction, and the presence of
bound or nearly-bound states. But for low-momentum interactions with cutoffs
around 2 fm^{-1}, the softened potential combined with Pauli blocking leads to
corrections in nuclear matter in the particle-particle channel that are well
converged at second order in the potential, suggesting that perturbation theory
can be used in place of Brueckner resummations. Calculations of nuclear matter
using the low-momentum two-nucleon force V_{low k} with a corresponding
leading-order three-nucleon (3N) force from chiral effective field theory (EFT)
exhibit nuclear binding in the Hartree-Fock approximation, and become less
cutoff dependent with the inclusion of the dominant second-order contributions.
The role of the 3N force is essential to obtain saturation, and the
contribution to the total potential energy is compatible with EFT
power-counting estimates.Comment: 24 pages, 7 figures, references and attractive c4 contribution added,
figures updated, conclusions unchanged; minor additions, to appear in Nucl.
Phys.
Low-momentum interactions with smooth cutoffs
Nucleon-nucleon potentials evolved to low momentum, which show great promise
in few- and many-body calculations, have generally been formulated with a sharp
cutoff on relative momenta. However, a sharp cutoff has technical disadvantages
and can cause convergence problems at the 10-100 keV level in the deuteron and
triton. This motivates using smooth momentum-space regulators as an
alternative. We generate low-momentum interactions with smooth cutoffs both
through energy-independent renormalization group methods and using a multi-step
process based on the Bloch-Horowitz approach. We find greatly improved
convergence for calculations of the deuteron and triton binding energies in a
harmonic oscillator basis compared to results with a sharp cutoff. Even a
slight evolution of chiral effective field theory interactions to lower momenta
is beneficial. The renormalization group preserves the long-range part of the
interaction, and consequently the renormalization of long-range operators, such
as the quadrupole moment, the radius and 1/r, is small. This demonstrates that
low-energy observables in the deuteron are reproduced without short-range
correlations in the wave function.Comment: 29 pages, 19 figure
Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry
The scalar and vector topological Yang-Mills symmetries determine a closed
and consistent sector of Yang-Mills supersymmetry. We provide a geometrical
construction of these symmetries, based on a horizontality condition on
reducible manifolds. This yields globally well-defined scalar and vector
topological BRST operators. These operators generate a subalgebra of maximally
supersymmetric Yang-Mills theory, which is small enough to be closed off-shell
with a finite set of auxiliary fields and large enough to determine the
Yang-Mills supersymmetric theory. Poincar\'e supersymmetry is reached in the
limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs
is thus removed by the requirement of scalar and vector topological symmetry,
which also determines the complete supersymmetry transformations in a twisted
way. Provided additional Killing vectors exist on the manifold, an equivariant
extension of our geometrical framework is provided, and the resulting
"equivariant topological field theory" corresponds to the twist of super
Yang-Mills theory on Omega backgrounds.Comment: 50 page
Field dependent nilpotent symmetry for gauge theories
We construct the field dependent mixed BRST (combination of BRST and
anti-BRST) transformations for pure gauge theories. These are shown to be an
exact nilpotent symmetry of both the effective action as well as the generating
functional for certain choices of the field dependent parameters. We show that
the Jacobian contributions for path integral measure in the definition of
generating functional arising from BRST and anti-BRST part compensate each
other. The field dependent mixed BRST transformations are also considered in
field/antifield formulation to show that the solutions of quantum master
equation remain invariant under these. Our results are supported by several
explicit examples.Comment: 25 pages, No figures, Revte
String Theoretic Bounds on Lorentz-Violating Warped Compactification
We consider warped compactifications that solve the 10 dimensional
supergravity equations of motion at a point, stabilize the position of a
D3-brane world, and admit a warp factor that violates Lorentz invariance along
the brane. This gives a string embedding of ``asymmetrically warped'' models
which we use to calculate stringy (\alpha') corrections to standard model
dispersion relations, paying attention to the maximum speeds for different
particles. We find, from the dispersion relations, limits on gravitational
Lorentz violation in these models, improving on current limits on the speed of
graviton propagation, including those derived from field theoretic loops. We
comment on the viability of models that use asymmetric warping for self-tuning
of the brane cosmological constant.Comment: 20pg, JHEP3; v2 additional references, slight change to intro; v3.
added referenc
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