64 research outputs found
Absence of gravitational contributions to the running Yang-Mills coupling
The question of a modification of the running gauge coupling of (non-)
abelian gauge theories by an incorporation of the quantum gravity contribution
has recently attracted considerable interest. In this letter we perform an
involved diagrammatical calculation in the full Einstein-Yang-Mills system both
in cut-off and dimensional regularization at one loop order. It is found that
all gravitational quadratic divergencies cancel in cut-off regularization and
are trivially absent in dimensional regularization so that there is no
alteration to asymptotic freedom at high energies. The logarithmic divergencies
give rise to an extended effective Einstein-Yang-Mills Lagrangian with a
counterterm of dimension six. In the pure Yang-Mills sector this counterterm
can be removed by a nonlinear field redefinition of the gauge potential,
reproducing a classical result of Deser, Tsao and van Nieuwenhuizen obtained in
the background field method with dimensional regularization.Comment: 4 pages, 1 figure, uses revtex and feynmf. v2: references adde
Loop calculations in quantum-mechanical non-linear sigma models
By carefully analyzing the relations between operator methods and the
discretized and continuum path integral formulations of quantum-mechanical
systems, we have found the correct Feynman rules for one-dimensional path
integrals in curved spacetime. Although the prescription how to deal with the
products of distributions that appear in the computation of Feynman diagrams in
configuration space is surprising, this prescription follows unambiguously from
the discretized path integral. We check our results by an explicit two-loop
calculation.Comment: 17 pages, LaTeX, and one figur
Coordinate representation of particle dynamics in AdS and in generic static spacetimes
We discuss the quantum dynamics of a particle in static curved spacetimes in
a coordinate representation. The scheme is based on the analysis of the squared
energy operator E^2, which is quadratic in momenta and contains a scalar
curvature term. Our main emphasis is on AdS spaces, where this term is fixed by
the isometry group. As a byproduct the isometry generators are constructed and
the energy spectrum is reproduced. In the massless case the conformal symmetry
is realized as well. We show the equivalence between this quantization and the
covariant quantization, based on the Klein-Gordon type equation in AdS. We
further demonstrate that the two quantization methods in an arbitrary
(N+1)-dimensional static spacetime are equivalent to each other if the scalar
curvature terms both in the operator E^2 and in the Klein-Gordon type equation
have the same coefficient equal to (N-1)/(4N).Comment: 14 pages, no figures, typos correcte
Collagen I-Matrigel Scaffolds for Enhanced Schwann Cell Survival and Control of Three-Dimensional Cell Morphology
We report on the ability to control three-dimensional Schwann cell (SC) morphology using collagen I Matrigel composite scaffolds for neural engineering applications. SCs are supportive of nerve regeneration after injury, and it has recently been reported that SCs embedded in collagen I, a material frequently used in guidance channel studies, do not readily extend processes, instead adopting a spherical morphology indicative of little interaction with the matrix. We have modified collagen I matrices by adding Matrigel to make them more supportive of SCs and characterized these matrices and SC morphology in vitro. Incorporation of 10%, 20%, 35%, and 50% Matrigel by volume resulted in 2.4, 3.5, 3.7, and 4.2 times longer average SC process length after 14 days in culture than with collagen I only controls. Additionally, only 35% and 50% Matrigel constructs were able to maintain SC number over 14 days, whereas an 88% decrease in cells from initial seeding density was observed in collagen-only constructs over the same time period. Mechanical testing revealed that the addition of 50% Matrigel increased matrix stiffness from 6.4kPa in collagen I only constructs to 9.8kPa. Furthermore, second harmonic generation imaging showed that the addition of Matrigel resulted in non-uniform distribution of collagen I, and scanning electron microscope imaging illustrated distinct differences in the fibrillar structure of the different constructs. Collectively, this work lays a foundation for developing scaffolding materials that are concurrently supportive of neurons and SCs for future neural engineering applications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78114/1/ten.tea.2008.0406.pd
On the quantum mechanics of M(atrix) theory
We present a study of M(atrix) theory from a purely canonical viewpoint. In
particular, we identify free particle asymptotic states of the model
corresponding to the supergraviton multiplet of eleven dimensional
supergravity. These states have a natural interpretation as excitations in the
flat directions of the matrix model potential. Furthermore, we provide the
split of the matrix model Hamiltonian into a free part describing the free
propagation of these particle states along with the interaction Hamiltonian
describing their interactions. Elementary quantum mechanical perturbation
theory then yields an effective potential for these particles as an expansion
in their inverse separation. Remarkably we find that the leading velocity
independent terms of the effective potential cancel in agreement with the fact
that there is no force between stationary D0 branes. The scheme we present
provides a framework in which one can perturbatively compute the M(atrix)
theory result for the eleven dimensional supergraviton S matrix.Comment: 28 pages, Latex2
Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral
The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right|
\exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, in
powers of can be made in a number of ways. For (the case of interest
when doing one-loop calculations) numerous approaches have been employed to
determine this expansion to very high order; when (relevant for
doing calculations beyond one-loop) there appear to be but two examples of
performing the DeWitt expansion. In this paper we compute the off-diagonal
elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge.
Our technique is based on representing by a quantum mechanical path
integral. We also generalize our method to the case of curved space, allowing
us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp
\case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i
A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of
normal coordinates. By comparison with results for the DeWitt expansion of this
matrix element obtained by the iterative solution of the diffusion equation,
the relative merit of different approaches to the representation of as a quantum mechanical path integral can be assessed. Furthermore, the
exact dependence of on some geometric scalars can be
determined. In two appendices, we discuss boundary effects in the
one-dimensional quantum mechanical path integral, and the curved space
generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects
for finite proper-time intervals; inclusion of these effects seem to make our
results consistent with those from explicit heat-kernel method
Harmonic BRST Quantization of Systems with Irreducible Holomorphic Boson and Fermion Constraints
We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing
bosonic systems with second-class constraints or first-class holomorphic
constraints extends to systems having both bosonic and fermionic second-class
or first-class holomorphic constraints. Using a limit argument, we show that
the harmonic BRST modified path integral reproduces the correct Senjanovic
measure.Comment: 11 pages, phyzz
Elimination of the spin supplementary condition in the effective field theory approach to the post-Newtonian approximation
The present paper addresses open questions regarding the handling of the spin
supplementary condition within the effective field theory approach to the
post-Newtonian approximation. In particular it is shown how the covariant spin
supplementary condition can be eliminated at the level of the potential (which
is subtle in various respects) and how the dynamics can be cast into a fully
reduced Hamiltonian form. Two different methods are used and compared, one
based on the well-known Dirac bracket and the other based on an action
principle. It is discussed how the latter approach can be used to improve the
Feynman rules by formulating them in terms of reduced canonical spin variables.Comment: 42 pages, document changed to match published version, in press; Ann.
Phys. (N. Y.) (2012
Loop calculations in quantum-mechanical non-linear sigma models sigma models with fermions and applications to anomalies
We construct the path integral for one-dimensional non-linear sigma models,
starting from a given Hamiltonian operator and states in a Hilbert space. By
explicit evaluation of the discretized propagators and vertices we find the
correct Feynman rules which differ from those often assumed. These rules, which
we previously derived in bosonic systems \cite{paper1}, are now extended to
fermionic systems. We then generalize the work of Alvarez-Gaum\'e and Witten
\cite{alwi} by developing a framework to compute anomalies of an
-dimensional quantum field theory by evaluating perturbatively a
corresponding quantum mechanical path integral. Finally, we apply this
formalism to various chiral and trace anomalies, and solve a series of
technical problems: the correct treatment of Majorana fermions in path
integrals with coherent states (the methods of fermion doubling and fermion
halving yield equivalent results when used in applications to anomalies),
a complete path integral treatment of the ghost sector of chiral
Yang-Mills anomalies, a complete path integral treatment of trace
anomalies, the supersymmetric extension of the Van Vleck determinant,
and a derivation of the spin- Jacobian of Alvarez-Gaum\'{e} and
Witten for Lorentz anomalies.Comment: 67 pages, LaTeX, with one figure (needs epsfig
- …