20 research outputs found
Mass loss by a scalar charge in an expanding universe
We study the phenomenon of mass loss by a scalar charge -- a point particle
that acts a source for a noninteracting scalar field -- in an expanding
universe. The charge is placed on comoving world lines of two cosmological
spacetimes: a de Sitter universe, and a spatially-flat, matter-dominated
universe. In both cases, we find that the particle's rest mass is not a
constant, but that it changes in response to the emission of monopole scalar
radiation by the particle. In de Sitter spacetime, the particle radiates all of
its mass within a finite proper time. In the matter-dominated cosmology, this
happens only if the charge of the particle is sufficiently large; for smaller
charges the particle first loses some of its mass, but then regains it all
eventually.Comment: 11 pages, RevTeX4, Accepted for Phys. Rev.
Geometric Origin of CP Violation in an Extra-Dimensional Brane World
The fermion mass hierarchy and finding a predictive mechanism of the flavor
mixing parameters remain two of the least understood puzzles facing particle
physics today. In this work, we demonstrate how the realization of the Dirac
algebra in the presence of two extra spatial dimensions leads to complex
fermion field profiles in the extra dimensions. Dimensionally reducing to four
dimensions leads to complex quark mass matrices in such a fashion that CP
violation necessarily follows. We also present the generalization of the
Randall-Sundrum scenario to the case of a multi-brane, six-dimensional
brane-world and discuss how multi-brane worlds may shed light on the generation
index of the SM matter content.Comment: 24 pages, 1 figure; references adde
CP Violation from Dimensional Reduction: Examples in 4+1 Dimensions
We provide simple examples of the generation of complex mass terms and hence
CP violation through dimensional reduction.Comment: 6 pages, typos corrected, 1 reference adde
Four-point Green functions in the Schwinger Model
The evaluation of the 4-point Green functions in the 1+1 Schwinger model is
presented both in momentum and coordinate space representations. The crucial
role in our calculations play two Ward identities: i) the standard one, and ii)
the chiral one. We demonstrate how the infinite set of Dyson-Schwinger
equations is simplified, and is so reduced, that a given n-point Green function
is expressed only through itself and lower ones. For the 4-point Green
function, with two bosonic and two fermionic external `legs', a compact
solution is given both in momentum and coordinate space representations. For
the 4-fermion Green function a selfconsistent equation is written down in the
momentum representation and a concrete solution is given in the coordinate
space. This exact solution is further analyzed and we show that it contains a
pole corresponding to the Schwinger boson. All detailed considerations given
for various 4-point Green functions are easily generizable to higher functions.Comment: In Revtex, 12 pages + 2 PostScript figure
A spatially-VSL gravity model with 1-PN limit of GRT
A scalar gravity model is developed according the 'geometric conventionalist'
approach introduced by Poincare (Einstein 1921, Poincare 1905, Reichenbach
1957, Gruenbaum1973). In principle this approach allows an alternative
interpretation and formulation of General Relativity Theory (GRT), with
distinct i) physical congruence standard, and ii) gravitation dynamics
according Hamilton-Lagrange mechanics, while iii) retaining empirical
indistinguishability with GRT. In this scalar model the congruence standards
have been expressed as gravitationally modified Lorentz Transformations
(Broekaert 2002). The first type of these transformations relate quantities
observed by gravitationally 'affected' (natural geometry) and 'unaffected'
(coordinate geometry) observers and explicitly reveal a spatially variable
speed of light (VSL). The second type shunts the unaffected perspective and
relates affected observers, recovering i) the invariance of the locally
observed velocity of light, and ii) the local Minkowski metric (Broekaert
2003). In the case of a static gravitation field the model retrieves the
phenomenology implied by the Schwarzschild metric. The case with proper source
kinematics is now described by introduction of a 'sweep velocity' field w: The
model then provides a hamiltonian description for particles and photons in full
accordance with the first Post-Newtonian approximation of GRT (Weinberg 1972,
Will 1993).Comment: v1: 11 pages, GR17 conf. paper, Dublin 2004, v2: WEP issue solved,
section on acceleration transformation added, text improved, more references,
same results, v3: typos removed, footnotes, added and references updated, v4:
appendix added, improved tex
Compton Scattering and the Spin Structure of the Nucleon at Low Energies
We analyze polarized Compton scattering which provides information on the
spin-structure of the nucleon. For scattering processes with photon energies up
to 100 MeV the spin-structure dependence can be encoded into four independent
parameters-the so-called spin-polarizabilities of the
nucleon, which we calculate within the framework of the "small scale expansion"
in SU(2) baryon chiral perturbation theory. Specific application is made to
"forward" and "backward" spin- polarizabilities.Comment: 8 pages revtex file, separation between pion-pole and regular
contributions detailed + minor wording changes, results and conclusions
unchange
Monotonicity of quantum ground state energies: Bosonic atoms and stars
The N-dependence of the non-relativistic bosonic ground state energy is
studied for quantum N-body systems with either Coulomb or Newton interactions.
The Coulomb systems are "bosonic atoms," with their nucleus fixed, and the
Newton systems are "bosonic stars". In either case there exists some third
order polynomial in N such that the ratio of the ground state energy to the
respective polynomial grows monotonically in N. Some applications of these new
monotonicity results are discussed
Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
We study quartic matrix models with partition function Z[E,J]=\int dM
\exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of
Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0
is a scalar coupling constant and the matrix J is used to generate correlation
functions. For E not a multiple of the identity matrix, we prove a universal
algebraic recursion formula which gives all higher correlation functions in
terms of the 2-point function and the distinct eigenvalues of E. The 2-point
function itself satisfies a closed non-linear equation which must be solved
case by case for given E. These results imply that if the 2-point function of a
quartic matrix model is renormalisable by mass and wavefunction
renormalisation, then the entire model is renormalisable and has vanishing
\beta-function.
As main application we prove that Euclidean \phi^4-quantum field theory on
four-dimensional Moyal space with harmonic propagation, taken at its
self-duality point and in the infinite volume limit, is exactly solvable and
non-trivial. This model is a quartic matrix model, where E has for N->\infty
the same spectrum as the Laplace operator in 4 dimensions. Using the theory of
singular integral equations of Carleman type we compute (for N->\infty and
after renormalisation of E,\lambda) the free energy density
(1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear
integral equation. Existence of a solution is proved via the Schauder fixed
point theorem.
The derivation of the non-linear integral equation relies on an assumption
which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae
and vanishing of \beta-function hold for general quartic matrix models. v3:
We add the existence proof for a solution of the non-linear integral
equation. A rescaling of matrix indices was necessary. v2: We provide
Schwinger-Dyson equations for all correlation functions and prove an
algebraic recursion formula for their solutio
Interaction of N solitons in the massive Thirring model and optical gap system: the Complex Toda Chain Model
Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton
interaction I show that the train propagation of N well separated solitons of
the massive Thirring model is described by the complex Toda chain with N nodes.
For the optical gap system a generalised (non-integrable) complex Toda chain is
derived for description of the train propagation of well separated gap
solitons. These results are in favor of the recently proposed conjecture of
universality of the complex Toda chain.Comment: RevTex, 23 pages, no figures. Submitted to Physical Review
Instantons and the infrared behavior of the fermion propagator in the Schwinger Model
Fermion propagator of the Schwinger Model is revisited from the point of view
of its infrared behavior. The values of anomalous dimensions are found in
arbitrary covariant gauge and in all contributing instanton sectors. In the
case of a gauge invariant, but path dependent propagator, the exponential
dependence, instead of power law one, is established for the special case when
the path is a straight line. The leading behavior is almost identical in any
sector, differing only by the slowly varying, algebraic prefactors. The other
kind of the gauge invariant function, which is the amplitude of the dressed
Dirac fermions, may be reduced, by the appropriate choice of the dressing, to
the gauge variant one, if Landau gauge is imposed.Comment: 9 pages, in REVTE