50 research outputs found
Finitely Many Dirac-Delta Interactions on Riemannian Manifolds
This work is intended as an attempt to study the non-perturbative
renormalization of bound state problem of finitely many Dirac-delta
interactions on Riemannian manifolds, S^2, H^2 and H^3. We formulate the
problem in terms of a finite dimensional matrix, called the characteristic
matrix. The bound state energies can be found from the characteristic equation.
The characteristic matrix can be found after a regularization and
renormalization by using a sharp cut-off in the eigenvalue spectrum of the
Laplacian, as it is done in the flat space, or using the heat kernel method.
These two approaches are equivalent in the case of compact manifolds. The heat
kernel method has a general advantage to find lower bounds on the spectrum even
for compact manifolds as shown in the case of S^2. The heat kernels for H^2 and
H^3 are known explicitly, thus we can calculate the characteristic matrix.
Using the result, we give lower bound estimates of the discrete spectrum.Comment: To be published in JM
On two dimensional coupled bosons and fermions
We study complex bosons and fermions coupled through a generalized Yukawa
type coupling in the large-N_c limit following ideas of Rajeev [Int. Jour. Mod.
Phys. A 9 (1994) 5583]. We study a linear approximation to this model. We show
that in this approximation we do not have boson-antiboson and
fermion-antifermion bound states occuring together. There is a possibility of
having only fermion-antifermion bound states. We support this claim by finding
distributional solutions with energies lower than the two mass treshold in the
fermion sector. This also has implications from the point of view of scattering
theory to this model. We discuss some aspects of the scattering above the two
mass treshold of boson pairs and fermion pairs. We also briefly present a
gauged version of the same model and write down the linearized equations of
motion.Comment: 25 pages, no figure
Large N limit of SO(N) gauge theory of fermions and bosons
In this paper we study the large N_c limit of SO(N_c) gauge theory coupled to
a Majorana field and a real scalar field in 1+1 dimensions extending ideas of
Rajeev. We show that the phase space of the resulting classical theory of
bilinears, which are the mesonic operators of this theory, is OSp_1(H|H
)/U(H_+|H_+), where H|H refers to the underlying complex graded space of
combined one-particle states of fermions and bosons and H_+|H_+ corresponds to
the positive frequency subspace. In the begining to simplify our presentation
we discuss in detail the case with Majorana fermions only (the purely bosonic
case is treated in our earlier work). In the Majorana fermion case the phase
space is given by O_1(H)/U(H_+), where H refers to the complex one-particle
states and H_+ to its positive frequency subspace. The meson spectrum in the
linear approximation again obeys a variant of the 't Hooft equation. The linear
approximation to the boson/fermion coupled case brings an additonal bound state
equation for mesons, which consists of one fermion and one boson, again of the
same form as the well-known 't Hooft equation.Comment: 27 pages, no figure
Supergrassmannian and large N limit of quantum field theory with bosons and fermions
We study a large N_{c} limit of a two-dimensional Yang-Mills theory coupled
to bosons and fermions in the fundamental representation. Extending an approach
due to Rajeev we show that the limiting theory can be described as a classical
Hamiltonian system whose phase space is an infinite-dimensional
supergrassmannian. The linear approximation to the equations of motion and the
constraint yields the 't Hooft equations for the mesonic spectrum. Two other
approximation schemes to the exact equations are discussed.Comment: 24 pages, Latex; v.3 appendix added, typos corrected, to appear in
JM
Existence of Hamiltonians for Some Singular Interactions on Manifolds
The existence of the Hamiltonians of the renormalized point interactions in
two and three dimensional Riemannian manifolds and that of a relativistic
extension of this model in two dimensions are proven. Although it is much more
difficult, the proof of existence of the Hamiltonian for the renormalized
resolvent for the non-relativistic Lee model can still be given. To accomplish
these results directly from the resolvent formula, we employ some basic tools
from the semigroup theory.Comment: 33 pages, no figure
Point Interaction in two and three dimensional Riemannian Manifolds
We present a non-perturbative renormalization of the bound state problem of n
bosons interacting with finitely many Dirac delta interactions on two and three
dimensional Riemannian manifolds using the heat kernel. We formulate the
problem in terms of a new operator called the principal or characteristic
operator. In order to investigate the problem in more detail, we then restrict
the problem to one particle sector. The lower bound of the ground state energy
is found for general class of manifolds, e.g., for compact and Cartan-Hadamard
manifolds. The estimate of the bound state energies in the tunneling regime is
calculated by perturbation theory. Non-degeneracy and uniqueness of the ground
state is proven by Perron-Frobenius theorem. Moreover, the pointwise bounds on
the wave function is given and all these results are consistent with the one
given in standard quantum mechanics. Renormalization procedure does not lead to
any radical change in these cases. Finally, renormalization group equations are
derived and the beta-function is exactly calculated. This work is a natural
continuation of our previous work based on a novel approach to the
renormalization of point interactions, developed by S. G. Rajeev.Comment: 43 page
Structure of the northwestern North Anatolian Fault Zone imaged via teleseismic scattering tomography
Information on fault zone structure is essential for our understanding of earthquake mechanics, continental deformation and seismic hazard. We use the scattered seismic wavefield to study the subsurface structure of the North Anatolian Fault Zone (NAFZ) in the region of the 1999 İzmit and Düzce ruptures using data from an 18-month dense deployment of seismometers with a nominal station spacing of 7 km. Using the forward- and back-scattered energy that follows the direct P-wave arrival from teleseismic earthquakes, we apply a scattered wave inversion approach and are able to resolve changes in lithospheric structure on a scale of 10 km or less in an area of about 130 km by 100 km across the NAFZ. We find several crustal interfaces that are laterally incoherent beneath the surface strands of the NAFZ and evidence for contrasting crustal structures either side of the NAFZ, consistent with the presence of juxtaposed crustal blocks and ancient suture zones. Although the two strands of the NAFZ in the study region strike roughly east–west, we detect strong variations in structure both north–south, across boundaries of the major blocks, and east–west, parallel to the strike of the NAFZ. The surface expression of the two strands of the NAFZ is coincident with changes on main interfaces and interface terminations throughout the crust and into the upper mantle in the tomographic sections. We show that a dense passive network of seismometers is able to capture information from the scattered seismic wavefield and, using a tomographic approach, to resolve the fine scale structure of crust and lithospheric mantle even in geologically complex regions. Our results show that major shear zones exist beneath the NAFZ throughout the crust and into the lithospheric mantle, suggesting a strong coupling of strain at these depths