21,218 research outputs found

    Model of supersymmetric quantum field theory with broken parity symmetry

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    Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form g(iϕ)2+δg(i\phi)^{2+\delta}, where δ\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 δ\delta is an even integer. This paper extends this idea to a two-dimensional supersymmetric quantum field theory whose superpotential is S(ϕ)=ig(iϕ)1+δ{\cal S}(\phi)=-ig(i\phi)^{1+\delta}. The resulting quantum field theory exhibits a broken parity symmetry for all δ>0\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

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    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 γ5\gamma_5 mass term the Hamiltonian is PT\cal PT-symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the PT\cal PT symmetry is unbroken, the spectrum of the quantum field theory is real. For the PT\cal PT-symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the PT\cal PT-symmetric scalar Sine-Gordon model, an exact construction of the C\cal C operator is given. It is shown that the PT\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

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    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 n2n^2 for large nn. 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

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    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=HH=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

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    To determine the Hilbert space and inner product for a quantum theory defined by a non-Hermitian PT\mathcal{PT}-symmetric Hamiltonian HH, it is necessary to construct a new time-independent observable operator called CC. It has recently been shown that for the {\it cubic} PT\mathcal{PT}-symmetric Hamiltonian H=p2+x2+iϵx3H=p^2+ x^2+i\epsilon x^3 one can obtain C\mathcal{C} as a perturbation expansion in powers of ϵ\epsilon. This paper considers the more difficult case of noncubic Hamiltonians of the form H=p2+x2(ix)δH=p^2+x^2(ix)^\delta (δ0\delta\geq0). For these Hamiltonians it is shown how to calculate C\mathcal{C} by using nonperturbative semiclassical methods.Comment: 11 pages, 1 figur

    Variational Ansatz for PT-Symmetric Quantum Mechanics

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    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

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    The spectrum of the Hermitian Hamiltonian 12p2+12m2x2+gx4{1\over2}p^2+{1\over2}m^2x^2+gx^4 (g>0g>0), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian H=12p2+12m2x2gx4H={1\over2}p^2+{1 \over2}m^2x^2-gx^4, where the coupling constant gg is real and positive, is PT{\cal PT}-symmetric. As a consequence, the spectrum of HH is known to be real and positive as well. Here, it is shown that there is a significant difference between these two theories: When gg 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 PT{\cal PT}-symmetric gϕ4-g\phi^4 quantum field theory for all dimensions 0D<30\leq D<3 but is not present in the conventional Hermitian gϕ4g\phi^4 field theory.Comment: 14 pages, 3figure

    Quantum tunneling as a classical anomaly

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    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''

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    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

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    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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