66 research outputs found
Pole structure of the Hamiltonian -function for a singular potential
We study the pole structure of the -function associated to the
Hamiltonian of a quantum mechanical particle living in the half-line
, subject to the singular potential . We show that
admits nontrivial self-adjoint extensions (SAE) in a given range of values
of the parameter . The -functions of these operators present poles
which depend on and, in general, do not coincide with half an integer (they
can even be irrational). The corresponding residues depend on the SAE
considered.Comment: 12 pages, 1 figure, RevTeX. References added. Version to appear in
Jour. Phys. A: Math. Ge
On the Vortex-Point Charge Composite: Classical Orbits and Quantum Bound States
The possibility of composite systems arising out of a point charge
interacting with a Nielsen-Olesen vortex in 2+1-dimensions is investigated. It
is shown that classical bounded orbits are possible for certain ranges of
parameters. Long lived metastable states are shown to exist, in a
semi-classical approach, from the study of the effective potential. Loss of
self-adjointness of the Hamiltonian and its subsequent self-adjoint extension
in some cases leads to bound states.Comment: 13 pages, Latex file, For figures e-mail to
"[email protected]
Quantum Fields in Hyperbolic Space-Times with Finite Spatial Volume
The one-loop effective action for a massive self-interacting scalar field is
investigated in -dimensional ultrastatic space-time ,
being a non-compact hyperbolic manifold with finite volume. Making
use of the Selberg trace formula, the -function related to the small
disturbance operator is constructed. For an arbitrary gravitational coupling,
it is found that has a simple pole at . The one-loop effective
action is analysed by means of proper-time regularisations and the one-loop
divergences are explicitly found. It is pointed out that, in this special case,
also -function regularisation requires a divergent counterterm, which
however is not necessary in the free massless conformal invariant coupling
case. Finite temperature effects are studied and the high-temperature expansion
is presented. A possible application to the problem of the divergences of the
entanglement entropy for a free massless scalar field in a Rindler-like
space-time is briefly discussed.Comment: 13 pages, LaTex. The contribution of hyperbolic elements has been
added. Other minor corrections and reference
Functional determinants for general self-adjoint extensions of Laplace-type operators resulting from the generalized cone
In this article we consider the zeta regularized determinant of Laplace-type
operators on the generalized cone. For {\it arbitrary} self-adjoint extensions
of a matrix of singular ordinary differential operators modelled on the
generalized cone, a closed expression for the determinant is given. The result
involves a determinant of an endomorphism of a finite-dimensional vector space,
the endomorphism encoding the self-adjoint extension chosen. For particular
examples, like the Friedrich's extension, the answer is easily extracted from
the general result. In combination with \cite{BKD}, a closed expression for the
determinant of an arbitrary self-adjoint extension of the full Laplace-type
operator on the generalized cone can be obtained.Comment: 27 pages, 2 figures; to appear in Manuscripta Mathematic
Quantum corrections to the mass of the supersymmetric vortex
We calculate quantum corrections to the mass of the vortex in N=2
supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a
box and apply the zeta function regularization. The boundary conditions
inevitably violate a part of the supersymmetries. Remaining supersymmetry is
however enough to ensure isospectrality of relevant operators in bosonic and
fermionic sectors. A non-zero correction to the mass of the vortex comes from
finite renormalization of couplings.Comment: Latex, 18 pp; v2 reference added; v3 minor change
Localisation of Fermions to brane: Codimension
We investigate dimensional fermionic models in which the system in
codimension- supports a topologically stable solution, and in which the
fermion may be localised to the brane, with power law in 'instanton'
backgrounds and exponentially in 'soliton' backgrounds. When the fermions are
isoscalars, the mechanism fails, while for isospinor fermions it is successful.
As backgrounds we consider instantons of Yang--Mills and sigma models in even
codimensions, solitons of sigma models in odd codimensions, as well as solitons
of Higgs and Goldstone models in all codimensions.Comment: 20 pages latex; expande
Thermal Fluctuations of Induced Fermion Number
We analyze the phemomenon of induced fermion number at finite temperature. At
finite temperature, the induced fermion number is a thermal expectation
value, and we compute the finite temperature fluctuations, . While the zero temperature induced fermion number is
topological and is a sharp observable, the finite temperature induced fermion
number is generically nontopological, and is not a sharp observable. The
fluctuations are due to the mixing of states inherent in any finite temperature
expectation value. We analyze in detail two different cases in 1+1 dimensional
field theory: fermions in a kink background, and fermions in a chiral sigma
model background. At zero temperature the induced fermion numbers for these two
cases are very similar, but at finite temperature they are very different. The
sigma model case is generic and the induced fermion number is nontopological,
but the kink case is special and the fermion number is topological, even at
finite temperature. There is a simple physical interpretation of all these
results in terms of the spectrum of the fermions in the relevant background,
and many of the results generalize to higher dimensional models.Comment: 17 pgs, 9 figs, RevTex
Testing Nonperturbative Orbifold Conjecture
We discuss Strassler's hypothesis of matching nonperturbative effects in
orbifold pairs of gauge theories which are perturbatively planar equivalent.
One of the examples considered is the parent N=1 SU(N) supersymmetric
Yang-Mills theory and its nonsupersymmetric orbifold daughter. We apply two
strategies allowing us to study nonperturbative effects: (i) low-energy
theorems; (ii) putting the theory on small-size T^4 or R^3 x S^1 the parent and
daughter theories are weakly coupled and amenable to quasiclassical treatment.
In all cases our consideration yields a mismatch between the parent and
daughter theories. Thus, regretfully, we present evidence against Strassler's
hypothesis.Comment: Latex, 13 pages, 1 eps figur
The ubiquitous -function and some of its "usual" and "unusual" meromorphic properties
In this contribution we announce a complete classification and new exotic
phenomena of the meromorphic structure of \z-functions associated to conic
manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic
extensions of these \z-functions have, in general, countably many logarithmic
branch cuts on the nonpositive real axis and unusual locations of poles with
arbitrarily large multiplicity. Moreover, we give a precise
algebraic-combinatorial formula to compute the coefficients of the leading
order terms of the singularities.Comment: Paper presented at the 8th Workshop on Quantum Field Theory under the
Influence of External Conditions (Leipzig, Germany, 16-21 September, 2007
Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction
A path-integral approach for delta-function potentials is presented.
Particular attention is paid to the two-dimensional case, which illustrates the
realization of a quantum anomaly for a scale invariant problem in quantum
mechanics. Our treatment is based on an infinite summation of perturbation
theory that captures the nonperturbative nature of the delta-function bound
state. The well-known singular character of the two-dimensional delta-function
potential is dealt with by considering the renormalized path integral resulting
from a variety of schemes: dimensional, momentum-cutoff, and real-space
regularization. Moreover, compatibility of the bound-state and scattering
sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations
were added for the sake of clarity; the main results and conclusions are
unchange
- …