21,218 research outputs found

### 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 $g(i\phi)^{2+\delta}$,
where $\delta$ 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 $\delta$ is an even integer. This paper extends
this idea to a two-dimensional supersymmetric quantum field theory whose
superpotential is ${\cal S}(\phi)=-ig(i\phi)^{1+\delta}$. The resulting quantum
field theory exhibits a broken parity symmetry for all $\delta>0$. 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

### 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 $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the
mass parameter this symmetry may be either broken or unbroken. When the $\cal
PT$ symmetry is unbroken, the spectrum of the quantum field theory is real. For
the $\cal PT$-symmetric version of the massive Thirring model in
two-dimensional space-time, which is dual to the $\cal PT$-symmetric scalar
Sine-Gordon model, an exact construction of the $\cal C$ operator is given. It
is shown that the $\cal PT$-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

### WKB Analysis of PT-Symmetric Sturm-Liouville problems

Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered
the Schroedinger eigenvalue problem on an infinite domain. This paper examines
the consequences of imposing the boundary conditions on a finite domain. As is
the case with regular Hermitian Sturm-Liouville problems, the eigenvalues of
the PT-symmetric Sturm-Liouville problem grow like $n^2$ for large $n$.
However, the novelty is that a PT eigenvalue problem on a finite domain
typically exhibits a sequence of critical points at which pairs of eigenvalues
cease to be real and become complex conjugates of one another. For the
potentials considered here this sequence of critical points is associated with
a turning point on the imaginary axis in the complex plane. WKB analysis is
used to calculate the asymptotic behaviors of the real eigenvalues and the
locations of the critical points. The method turns out to be surprisingly
accurate even at low energies.Comment: 11 pages, 8 figure

### Introduction to PT-Symmetric Quantum Theory

In most introductory courses on quantum mechanics one is taught that the
Hamiltonian operator must be Hermitian in order that the energy levels be real
and that the theory be unitary (probability conserving). To express the
Hermiticity of a Hamiltonian, one writes $H=H^\dagger$, where the symbol
$\dagger$ denotes the usual Dirac Hermitian conjugation; that is, transpose and
complex conjugate. In the past few years it has been recognized that the
requirement of Hermiticity, which is often stated as an axiom of quantum
mechanics, may be replaced by the less mathematical and more physical
requirement of space-time reflection symmetry (PT symmetry) without losing any
of the essential physical features of quantum mechanics. Theories defined by
non-Hermitian PT-symmetric Hamiltonians exhibit strange and unexpected
properties at the classical as well as at the quantum level. This paper
explains how the requirement of Hermiticity can be evaded and discusses the
properties of some non-Hermitian PT-symmetric quantum theories

### 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 $\mathcal{PT}$-symmetric Hamiltonian $H$, it is necessary to
construct a new time-independent observable operator called $C$. It has
recently been shown that for the {\it cubic} $\mathcal{PT}$-symmetric
Hamiltonian $H=p^2+ x^2+i\epsilon x^3$ one can obtain $\mathcal{C}$ as a
perturbation expansion in powers of $\epsilon$. This paper considers the more
difficult case of noncubic Hamiltonians of the form $H=p^2+x^2(ix)^\delta$
($\delta\geq0$). For these Hamiltonians it is shown how to calculate
$\mathcal{C}$ by using nonperturbative semiclassical methods.Comment: 11 pages, 1 figur

### Variational Ansatz for PT-Symmetric Quantum Mechanics

A variational calculation of the energy levels of a class of PT-invariant
quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 -
(ix)^N with N positive and x complex is presented. Excellent agreement is
obtained for the ground state and low lying excited state energy levels and
wave functions. We use an energy functional with a three parameter class of
PT-symmetric trial wave functions in obtaining our results.Comment: 9 pages -- one postscript figur

### Bound States of Non-Hermitian Quantum Field Theories

The spectrum of the Hermitian Hamiltonian ${1\over2}p^2+{1\over2}m^2x^2+gx^4$
($g>0$), which describes the quantum anharmonic oscillator, is real and
positive. The non-Hermitian quantum-mechanical Hamiltonian $H={1\over2}p^2+{1
\over2}m^2x^2-gx^4$, where the coupling constant $g$ is real and positive, is
${\cal PT}$-symmetric. As a consequence, the spectrum of $H$ is known to be
real and positive as well. Here, it is shown that there is a significant
difference between these two theories: When $g$ 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 ${\cal
PT}$-symmetric $-g\phi^4$ quantum field theory for all dimensions $0\leq D<3$
but is not present in the conventional Hermitian $g\phi^4$ field theory.Comment: 14 pages, 3figure

### Quantum tunneling as a classical anomaly

Classical mechanics is a singular theory in that real-energy classical
particles can never enter classically forbidden regions. However, if one
regulates classical mechanics by allowing the energy E of a particle to be
complex, the particle exhibits quantum-like behavior: Complex-energy classical
particles can travel between classically allowed regions separated by potential
barriers. When Im(E) -> 0, the classical tunneling probabilities persist.
Hence, one can interpret quantum tunneling as an anomaly. A numerical
comparison of complex classical tunneling probabilities with quantum tunneling
probabilities leads to the conjecture that as ReE increases, complex classical
tunneling probabilities approach the corresponding quantum probabilities. Thus,
this work attempts to generalize the Bohr correspondence principle from
classically allowed to classically forbidden regions.Comment: 12 pages, 7 figure

### Comment on ``Structure of exotic nuclei and superheavy elements in a relativistic shell model''

A recent paper [M. Rashdan, Phys. Rev. C 63, 044303 (2001)] introduces the
new parameterization NL-RA1 of the relativistic mean-field model which is
claimed to give a better description of nuclear properties than earlier ones.
Using this model ^{298}114 is predicted to be a doubly-magic nucleus. As will
be shown in this comment these findings are to be doubted as they are obtained
with an unrealistic parameterization of the pairing interaction and neglecting
ground-state deformation.Comment: 2 pages REVTEX, 3 figures, submitted to comment section of Phys. Rev.
C. shortened and revised versio

### Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

Conventional weak-coupling perturbation theory suffers from problems that
arise from resonant coupling of successive orders in the perturbation series.
Multiple-scale perturbation theory avoids such problems by implicitly
performing an infinite reordering and resummation of the conventional
perturbation series. Multiple-scale analysis provides a good description of the
classical anharmonic oscillator. Here, it is extended to study the Heisenberg
operator equations of motion for the quantum anharmonic oscillator. The
analysis yields a system of nonlinear operator differential equations, which is
solved exactly. The solution provides an operator mass renormalization of the
theory.Comment: 12 pages, Revtex, no figures, available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.htm

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