15 research outputs found
The euclidean propagator in a model with two non-equivalent instantons
We consider in detail how the quantum-mechanical tunneling phenomenon occurs
in a well-behaved octic potential. Our main tool will be the euclidean
propagator just evaluated between two minima of the potential at issue. For
such a purpose we resort to the standard semiclassical approximation which
takes into account the fluctuations over the instantons, i.e. the finite-action
solutions of the euclidean equation of motion. As regards the one-instanton
approach, the functional determinant associated with the so-called stability
equation is analyzed in terms of the asymptotic behaviour of the zero-mode. The
conventional ratio of determinants takes as reference the harmonic oscillator
whose frequency is the average of the two different frequencies derived from
the minima of the potential involved in the computation. The second instanton
of the model is studied in a similar way. The physical effects of the
multi-instanton configurations are included in this context by means of the
alternate dilute-gas approximation where the two instantons participate to
provide us with the final expression of the propagator.Comment: RevTex, 13 page
Analysis of nonperturbative fluctuations in a triple-well potential
We consider the quantum tunneling phenomenon in a well-behaved triple-well
potential. As required by the semiclassical approximation we take into account
the quadratic fluctuations over the instanton which represents as usual the
localised finite-action solution of the euclidean equation of motion. The
determinants of the quadratic differential operators at issue are evaluated by
means of the Gelfang-Yaglom method. In doing so the explicit computation of the
conventional ratio of determinants takes as reference the harmonic oscillator
whose frequency is the average of the individual frequencies derived from the
non-equivalent minima of the potential. Eventually the physical effects of the
multi-instanton configurations are included in this approach. As a matter of
fact we obtain information about the energies of the ground-state and the two
first excited levels of the discrete spectrum at issue.Comment: 12 pages, RevTe
Symmetric Triple Well with Non-Equivalent Vacua: Instantonic Approach
We show that for the triple well potential with non-equivalent vacua,
instantons generate for the low lying energy states a singlet and a doublet of
states rather than a triplet of equal energy spacing. Our energy splitting
formulae are also confirmed numerically. This splitting property is due to the
presence of non-equivalent vacua. A comment on its generality to multi-well is
presented.Comment: 10 pages, 3 figures, 2 tables; minor changes; added reference
Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface terms
We calculate the one-loop quantum corrections to the mass and central charge
of N=2 and N=4 supersymmetric monopoles in 3+1 dimensions. The corrections to
the N=2 central charge are finite and due to an anomaly in the conformal
central charge current, but they cancel for the N=4 monopole. For the quantum
corrections to the mass we start with the integral over the expectation value
of the Hamiltonian density, which we show to consist of a bulk contribution
which is given by the familiar sum over zero-point energies, as well as surface
terms which contribute nontrivially in the monopole sector. The bulk
contribution is evaluated through index theorems and found to be nonvanishing
only in the N=2 case. The contributions from the surface terms in the
Hamiltonian are cancelled by infinite composite operator counterterms in the
N=4 case, forming a multiplet of improvement terms. These counterterms are also
needed for the renormalization of the central charge. However, in the N=2 case
they cancel, and both the improved and the unimproved current multiplet are
finite.Comment: 1+40 pages, JHEP style. v2: small corrections and additions,
references adde
One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
We consider domain walls obtained by embedding the 1+1-dimensional
-kink in higher dimensions. We show that a suitably adapted dimensional
regularization method avoids the intricacies found in other regularization
schemes in both supersymmetric and non-supersymmetric theories. This method
allows us to calculate the one-loop quantum mass of kinks and surface tensions
of kink domain walls in a very simple manner, yielding a compact d-dimensional
formula which reproduces many of the previous results in the literature. Among
the new results is the nontrivial one-loop correction to the surface tension of
a 2+1 dimensional N=1 supersymmetric kink domain wall with chiral domain-wall
fermions.Comment: 23 pages, LATeX; v2: 25 pages, 2 references added, extended
discussion of renormalization schemes which dispels apparent contradiction
with previous result
N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -
We investigate particular models which can be N-fold supersymmetric at
specific values of a parameter in the Hamiltonians. The models to be
investigated are a periodic potential and a parity-symmetric sextic triple-well
potential. Through the quantitative analyses on the non-perturbative
contributions to the spectra by the use of the valley method, we show how the
characteristic features of N-fold supersymmetry which have been previously
reported by the authors can be observed. We also clarify the difference between
quasi-exactly solvable and quasi-perturbatively solvable case in view of the
dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX
Transmutations and spectral parameter power series in eigenvalue problems
We give an overview of recent developments in Sturm-Liouville theory
concerning operators of transmutation (transformation) and spectral parameter
power series (SPPS). The possibility to write down the dispersion
(characteristic) equations corresponding to a variety of spectral problems
related to Sturm-Liouville equations in an analytic form is an attractive
feature of the SPPS method. It is based on a computation of certain systems of
recursive integrals. Considered as families of functions these systems are
complete in the -space and result to be the images of the nonnegative
integer powers of the independent variable under the action of a corresponding
transmutation operator. This recently revealed property of the Delsarte
transmutations opens the way to apply the transmutation operator even when its
integral kernel is unknown and gives the possibility to obtain further
interesting properties concerning the Darboux transformed Schr\"{o}dinger
operators.
We introduce the systems of recursive integrals and the SPPS approach,
explain some of its applications to spectral problems with numerical
illustrations, give the definition and basic properties of transmutation
operators, introduce a parametrized family of transmutation operators, study
their mapping properties and construct the transmutation operators for Darboux
transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1111.444
The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach
The ground, one- and two-particle states of the (1+1)-dimensional massive
sine-Gordon field theory are investigated within the framework of the Gaussian
wave-functional approach. We demonstrate that for a certain region of the
model-parameter space, the vacuum of the field system is asymmetrical.
Furthermore, it is shown that two-particle bound state can exist upon the
asymmetric vacuum for a part of the aforementioned region. Besides, for the
bosonic equivalent to the massive Schwinger model, the masses of the one boson
and two-boson bound states agree with the recent second-order results of a
fermion-mass perturbation calculation when the fermion mass is small.Comment: Latex, 11 pages, 8 figures (EPS files