共查询到20条相似文献,搜索用时 562 毫秒
1.
Carl M. Bender 《Czechoslovak Journal of Physics》2006,56(9):1047-1062
In this paper, two independent methods are used to show that the non-Hermitian
-symmetric wrong-sign quartic Hamiltonian H = (1/2m)p
2 − gx
4 is exactly equivalent to the conventional Hermitian Hamiltonian
. First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated
by using functional-integration methods. As the linear term in the Hermitian Hamiltonian
is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly
is a consequence of the broken parity symmetry of the original non-Hermitian
-symmetric Hamiltonian. The anomaly term in
remains unchanged if an x
2 term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in
are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states. 相似文献
2.
Emanuela Caliceti 《Czechoslovak Journal of Physics》2005,55(9):1077-1080
Some recent results are described on the reality of the spectrum of
-symmetric Schrodinger operators, obtained by perturbing a class of quantum nonlinear oscillators by means of suitable relatively
bounded perturbations.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
3.
General point interactions for the second derivative operator in one dimension are studied. In particular,
-self-adjoint point interactions with the support at the origin and at points ±l are considered. The spectrum of such non-Hermitian operators is investigated and conditions when the spectrum is pure real are presented. The results are compared with those for standard self-adjoint point interactions. 相似文献
4.
5.
Carl M. Bender 《Czechoslovak Journal of Physics》2005,55(9):1067-1074
The Lee model is an elementary quantum field theory in which mass, wave-function, and charge renormalization can be performed
exactly. In early studies of this model in the 1950's it was found that there is a critical value of g
2, the square of the renormalized coupling constant, above which g
0
2
, the square of the unrenormalized coupling constant, is negative. For g
2 larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. In this non-Hermitian regime a new
state appears whose norm is negative. This state is called a ghost. It has always been thought that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears
to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess
symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having
symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a time-independent
operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore,
it has been shown that time evolution in such a theory is unitary. In this talk the C operator for the Lee model in the ghost regime is constructed in the V/Nθ sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum
field theory for all values of g
2.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
6.
Chains of extended twists are composed of factors
. The set of Jordanian twists {
} can be applied to the initial Hopf algebra
. In this case the remaining (transformed) factors of the chain can serve as extensions for such a multijordanian twist. We study the properties of these generalized extensions and the spectra of deformations of the corresponding Heisenberg-like algebras. The results are explicitly demonstrated for the case when
. 相似文献
7.
Miloslav Znojil 《Czechoslovak Journal of Physics》2006,56(9):977-984
A review of a few recent developments in our analysis and applications of the coupled-channel version of the formalism of
-symmetric quantum mechanics is given. 相似文献
8.
D. Arnaudon 《Czechoslovak Journal of Physics》1997,47(11):1075-1082
Irreducible representations of
at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra
not to be completely diagonalised. Some irreducible representations of
indeed contain indecomposable
-modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation. 相似文献
9.
To lowest order of perturbation theory we show that an equivalence can be established between a
-symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian h. An important feature of h is that it reveals a domain of couplings where the quartic potential could be attractive, vanishing or repulsive. We also
determine the associated physical quantities. 相似文献
10.
Lucy Gow 《Czechoslovak Journal of Physics》2005,55(11):1415-1420
Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y
of the general linear Lie algebra
. In this article, we extend some of their ideas to consider the Yangian Y
of the Lie superalgebra
. In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
11.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
12.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 相似文献
13.
Hitoshi Konno 《Czechoslovak Journal of Physics》2005,55(11):1455-1460
We give a level-2 representation of the elliptic algebra
in terms of one free boson and one free fermion. We show that
-modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the
coset
.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
14.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
15.
Recently, a class of
-invariant scalar quantum field theories described by the non-Hermitian Lagrangian
=
()
2
+g
2
(i) was studied. It was found that there are two regions of . For <0 the
-invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For 0 the
-invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle transition at =0 is not well understood. In this paper we initiate an investigation of this transition by carrying out a detailed numerical study of the effective potential V
eff
(c) in zero-dimensional spacetime. Although this numerical work reveals some differences between the <0 and the >0 regimes, we cannot yet see convincing evidence of the transition at =0 in the structure of the effective potential for
-symmetric quantum field theories. 相似文献
16.
We prove a simple formula for the transverse Poisson structure to a coadjoint orbit (in the dual of a Lie algebra
) and use it in examples such as
and
. We also give a sufficient condition on the isotropy subalgebra of
so that the transverse Poisson structureto the coadjoint orbit of is linear. 相似文献
17.
The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy
(where
0$$
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and
0$$
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are two constants). In particular, the perpendicular incidence of an electron with a given value
of the wave vector
is considered. The electron is forward-scattered into the region behind the barrier (region 2:
0$$
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), i. e. the wave function
is composed of plane waves with all wave vectors
such that
and
\left. 0 \right)} $$
" align="middle" border="0">
) (where
). Therefore, if
0$$
" align="middle" border="0">
, the wave function of the electron is represented as
, where
. An approximate formula is derived for the amplitude
. The authors pay a special attention to the flow density
and calculate this function in two cases: 1. for the plane
and 2. for high values of
is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier. 相似文献
18.
The purpose of this Letter is to develop further the Gauss diagram approach to finite-type link invariants. In this context we introduce Gauss diagrams counterparts to chord diagrams, 4T relation, weight systems arising from Lie algebras, and an algebra of unitrivalent graphs modulo the STU relation. The counterparts, respectively, are arrow diagrams, 6T relation, weights arising from the solutions of the classical Yang–Baxter equation, and an algebra
of acyclic arrow graphs (modulo an oriented version
of the STU relation). The algebra
encodes, in a graphical form, the main properties of Lie bialgebras, similarly to the well-known relation of the algebra of unitrivalent graphs to Lie algebras. We show that the oriented
and
relations hold, and that
is isomorphic to the algebra
of arrow diagrams. As an application, we consider an appropriate link-homotopy version
of the algebra
. Using this algebra, we construct a Gauss diagram invariants of string links up to link-homotopy, with values both in the algebra
and in . We observe that this construction gives the universal Milnor's link-homotopy -invariants. 相似文献
19.
We study the fractional decomposition of the quantum enveloping affine algebras
and
with vanishing central charge in the limit
. This decomposition is based on the bosonic representation and can be related to fractional supersymmetry and k-fermionic spin. The quantum affine algebras and the classical ones are equivalent in the fermionic realization. 相似文献
20.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献