57,946 research outputs found
Dual PT-Symmetric Quantum Field Theories
Some quantum field theories described by non-Hermitian Hamiltonians are
investigated. It is shown that for the case of a free fermion field theory with
a mass term the Hamiltonian is -symmetric. Depending on the
mass parameter this symmetry may be either broken or unbroken. When the symmetry is unbroken, the spectrum of the quantum field theory is real. For
the -symmetric version of the massive Thirring model in
two-dimensional space-time, which is dual to the -symmetric scalar
Sine-Gordon model, an exact construction of the operator is given. It
is shown that the -symmetric massive Thirring and Sine-Gordon models
are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon
models with appropriately shifted masses.Comment: 9 pages, 1 figur
Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
To determine the Hilbert space and inner product for a quantum theory defined
by a non-Hermitian -symmetric Hamiltonian , it is necessary to
construct a new time-independent observable operator called . It has
recently been shown that for the {\it cubic} -symmetric
Hamiltonian one can obtain as a
perturbation expansion in powers of . This paper considers the more
difficult case of noncubic Hamiltonians of the form
(). For these Hamiltonians it is shown how to calculate
by using nonperturbative semiclassical methods.Comment: 11 pages, 1 figur
Bound States of Non-Hermitian Quantum Field Theories
The spectrum of the Hermitian Hamiltonian
(), which describes the quantum anharmonic oscillator, is real and
positive. The non-Hermitian quantum-mechanical Hamiltonian , where the coupling constant is real and positive, is
-symmetric. As a consequence, the spectrum of is known to be
real and positive as well. Here, it is shown that there is a significant
difference between these two theories: When is sufficiently small, the
latter Hamiltonian exhibits a two-particle bound state while the former does
not. The bound state persists in the corresponding non-Hermitian -symmetric quantum field theory for all dimensions
but is not present in the conventional Hermitian field theory.Comment: 14 pages, 3figure
Periodic orbits for classical particles having complex energy
This paper revisits earlier work on complex classical mechanics in which it
was argued that when the energy of a classical particle in an analytic
potential is real, the particle trajectories are closed and periodic, but that
when the energy is complex, the classical trajectories are open. Here it is
shown that there is a discrete set of eigencurves in the complex-energy plane
for which the particle trajectories are closed and periodic.Comment: 12 pages, 9 figure
A PT-Invariant Potential With Complex QES Eigenvalues
We show that the quasi-exactly solvable eigenvalues of the Schr\"odinger
equation for the PT-invariant potential are
complex conjugate pairs in case the parameter M is an even integer while they
are real in case M is an odd integer. We also show that whereas the PT symmetry
is spontaneously broken in the former case, it is unbroken in the latter case.Comment: 8 pages, Latex, No fig, To appear in PLA(2000
Microscopic models for exotic nuclei
Starting from successful self-consistent mean-field models, this paper
discusses why and how to go beyond the mean field approximation. To include
long-range correlations from fluctuations in collective degrees of freedom, one
has to consider symmetry restoration and configuration mixing, which give
access to ground-state correlations and spectroscopy.Comment: invited talk at ENAM0
Exact solution for Morse oscillator in PT-symmetric quantum mechanics
The recently proposed PT-symmetric quantum mechanics works with complex
potentials which possess, roughly speaking, a symmetric real part and an
anti-symmetric imaginary part. We propose and describe a new exactly solvable
model of this type. It is defined as a specific analytic continuation of the
shape-invariant potential of Morse. In contrast to the latter well-known
example, all the new spectrum proves real, discrete and bounded below. All its
three separate subsequences are quadratic in n.Comment: 8 pages, submitted to Phys. Lett.
Complex periodic potentials with real band spectra
This paper demonstrates that complex PT-symmetric periodic potentials possess
real band spectra. However, there are significant qualitative differences in
the band structure for these potentials when compared with conventional real
periodic potentials. For example, while the potentials V(x)=i\sin^{2N+1}(x),
(N=0, 1, 2, ...), have infinitely many gaps, at the band edges there are
periodic wave functions but no antiperiodic wave functions. Numerical analysis
and higher-order WKB techniques are used to establish these results.Comment: 8 pages, 7 figures, LaTe
Model of supersymmetric quantum field theory with broken parity symmetry
Recently, it was observed that self-interacting scalar quantum field theories
having a non-Hermitian interaction term of the form ,
where is a real positive parameter, are physically acceptable in the
sense that the energy spectrum is real and bounded below. Such theories possess
PT invariance, but they are not symmetric under parity reflection or time
reversal separately. This broken parity symmetry is manifested in a nonzero
value for , even if is an even integer. This paper extends
this idea to a two-dimensional supersymmetric quantum field theory whose
superpotential is . The resulting quantum
field theory exhibits a broken parity symmetry for all . However,
supersymmetry remains unbroken, which is verified by showing that the
ground-state energy density vanishes and that the fermion-boson mass ratio is
unity.Comment: 20 pages, REVTeX, 11 postscript figure
Overcritical PT-symmetric square well potential in the Dirac equation
We study scattering properties of a PT-symmetric square well potential with
real depth larger than the threshold of particle-antiparticle pair production
as the time component of a vector potential in the (1+1)-dimensional Dirac
equation.Comment: 11 pages, 1 figure, to appear in Physics Letters
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