共查询到20条相似文献,搜索用时 15 毫秒
1.
H. J. de Vega 《Communications in Mathematical Physics》1979,70(1):29-42
When one tries to compute large orders in the 1/N series à la Lipatov a complicated non-linear equation for the instanton is found in ø4 or non-linear sigma models.We solve here this equation in the one-dimensional case (quantum mechanics) by inverse scattering techniques. From the instanton solutions we obtain theK
th order of the 1/N perturbation theory up to 0(K
–1) for the 0(N) symmetric anharmonic oscillator and up to a factor 0(K
0) for a non-symmetric model. In the symmetric case we agree with results recently obtained in quantum mechanics by Hikami and Brézin following a different procedure. For the non-symmetric anharmonic oscillator we believe our formulae are new. 相似文献
2.
Maia Angelova 《Acta Physica Hungarica A》2004,19(3-4):347-351
An algebraic model based on Lie-algebraic techniques is applied to vibrational molecular thermodynamics. The model uses the isomorphism between the SU(2) algebra and the one-dimensional Morse oscillator. A vibrational high-temperature partition function and the related thermodynamic properties are derived in terms of the parameters of the model. The anharmonic vibrations are described as anharmonic q-bosons using a first-order expansion of a quantum deformation. It is shown, that this quantum deformation is related to the shape of the Morse potential. 相似文献
3.
A method, independently proposed by Kaiser and by us, to study the strong coupling limit of the Green functions is described and discussed. Although its quantum mechanical version exhibits unusual features, an application to the anharmonic oscillator indicates that the method is able to reproduce correctly known numerical results. In spite of difficulties in the setting up of a renormalization program for the theory, a preliminary study of the CS β function for the gφ4 interaction shows that is asymptotically linear in the renormalization coupling constant. Evidence is given for the compatibility of this behaviour with the information that can be drawn from the known perturbative expansion. 相似文献
4.
A new and simple method to expand the anharmonic vibrational wave functions with respect to the harmonic oscillator wave functions is proposed. The coefficients of the expansion are given as matrix elements of the S function of the contact transformation in the perturbation theory and the explicit expressions of these coefficients are given within the approximation to the second order in λ. As an example of the expansion, the wave functions of water molecules were calculated and applied to the calculation of infrared band intensities and average values of dipole moments in several states. 相似文献
5.
We present the result for the invariant
factor of K0–
mixing in the chiral limit and to next-to-leading order in the 1/Nc expansion. We explicitly demonstrate the cancellation of the renormalization scale and scheme dependences between short- and long-distance contributions in the final expression. Numerical estimates are then given, by taking into account increasingly refined short- and long-distance constraints of the underlying QCD Green's function which governs the
factor. 相似文献
6.
Analysis of the energy distribution in an ensemble of quantum anharmonic oscillators loaded by an external force in a wide
temperature range (from T = 0) is carried out using a general approach based on the virial theorem. At T = 0, anharmonic effects are observed: a linear variation of zero-point energy of an oscillator under loading (energy decrease
during extension and increase under compression) and a linear variation of the average kinetic and potential energy components.
At high temperatures, at which the dynamics of the oscillators becomes classical, the anharmonic effects are manifested in
a linear variation in the vibrational energy and a linear variation in the average kinetic and potential energy components
upon an increase in force. Mutually compensating variation in the average kinetic and potential energy components of the internal
dynamic energy of an oscillator (energy redistribution upon loading) takes place both at low and high temperatures. 相似文献
7.
8.
《Physics letters. A》2001,286(4):261-276
An analytical solution up to the second order in the coupling constant λ is obtained for a classical quartic anharmonic oscillator by using Taylor series method. Our solution yields, as a special instance, the corresponding results obtained by using Laplace transform. With the help of correspondence principle, the classical solution is used to obtain the solution corresponding to a quantum quartic anharmonic oscillator. In the weak coupling regime (i.e., anharmonic constant λ⪡1), the so-called secular terms in classical and quantum solutions are tucked in (summed up) to avoid the nonconvergence. Both the classical and quantum solutions are used to obtain the frequency shifts of the quartic oscillators. It is found that these frequency shifts coincide exactly with those of the earlier results obtained by other methods. From the quantum field theoretic point of view, our solution exhibits the so-called Lamb shift. As an application of the solution for the quantum oscillator, we examine the possibility of getting squeezed states out of the input coherent light interacting with a nonlinear medium of inversion symmetry. 相似文献
9.
Hee-Jung Lee Chang Ho Hyun Chang-Hwan Lee Hyun-Chul Kim 《The European Physical Journal C - Particles and Fields》2006,45(2):451-457
We investigate the ΔS = 0 effective chiral Lagrangian from the instanton vacuum. Based on the ΔS = 0 effective weak Hamiltonian from the operator product expansion and renormalization group equations, we derive the strangeness-conserving
effective weak chiral Lagrangian from the instanton vacuum to order
and the next-to-leading order in the 1/Nc expansion at the quark level. We find that the quark condensate and a dynamical term which arise from the QCD and electroweak
penguin operators appear in the next-to-leading order in the 1/Nc expansion for the ΔS = 0 effective weak chiral Lagrangian, while they are in the leading order terms in the ΔS = 1 case. Three different types of form factors are employed and we find that the dependence on the different choices of
the form factor is rather insensitive. The low-energy constants of the Gasser-Leutwyler type are determined and discussed
in the chiral limit.
Arrival of the final proofs: 2 December 2005
PACS:
12.40.-y, 14.20.Dh 相似文献
10.
Heinz Horner 《Zeitschrift für Physik A Hadrons and Nuclei》1967,205(1):72-89
A theory of lattice dynamics for quantum crystals is developed. This is done by summing an infinite class of diagrams of the usual anharmonic expansion and by avoiding the harmonic approximation as starting point. The zero order of the expansion given in this paper corresponds to the harmonic approximation with an effective potential. Higher orders correspond to higher anharmonic corrections with the same potential. Since the new potential varies more slowly the expansion seems to converge more rapidly than the usual anharmonic expansion. Numerical calculations on bcc He3 show that the ground state energy is lowered by about 3–4 cal/mol by taking into account long range correlations due to phonons. The elastic constants and the Debye temperature are calculated in zero and second order. The lowering of the bulk modulus due to the second order is about 10%. Experiments agree quite well with the second order results. 相似文献
11.
W. K. McClary 《Communications in Mathematical Physics》1972,24(3):171-179
A class of perturbation problems is considered, in which the Rayleigh-Schrödinger perturbation series for the ground state eigenvalue and eigenvector are presumed to diverge. This class includes the (:2m
:g(x))2, (m=2, 3) quantum field theory models and the quantum mechanical anharmonic oscillator. It is shown that, using matrix elements and vectors which occur in the series coefficients, one may construct convergent approximants to the eigenvalue and eigenvector. Results of a calculation of the ground state energy of thex
4 anharmonic oscillator are given.Supported in part by the National Research Council of Canada. 相似文献
12.
I. Ya. Aref'eva E. R. Nissimov S. J. Pacheva 《Communications in Mathematical Physics》1980,71(3):213-246
A modified soft mass renormalization scheme for 1/N expansion of the three dimensionalO(N)-invariant chiral field in the high- and low-temperature phases, as well as at the critical point, is constructed, free of infrared divergencies in each separate diagram. Generalized quantum chirality identities for composite operators are derived, from which the renormalizability of the model follows. The approach formulated here is applied to a rigorous analysis of the universal critical behaviour of theN-component chiral field in three dimensions. 相似文献
13.
U. Ritschel 《Zeitschrift fur Physik C Particles and Fields》1991,51(3):469-475
In order to study the effects of renormalization on the variationally calculated φ4 effective potential, we employ the Gaussian-effective-potential formalism, nonlinear canonical transformations, and the loop approximation. A quantitative comparison of physically equivalent potentials is carried out in two dimensions. The renormalization procedure in three dimensions, leading after the nonlinear transformation to a manifestly finite energy expectation, is described. Different from finite-dimensional quantum mechanics, the optimization is meaningful only if all divergent sub-graphs generated by the ansatz are identified and renormalized by the bare parameters. 相似文献
14.
The total hadronic decay width of the Weinberg-Salam type Higgs boson is estimated in QCD for the Higgs boson mass much larger than the ordinary hadronic mass scale, by use of the operator product expansion and renormalization group equation. We give an explicit formula for the decay width in terms of quark masses including strong interaction corrections up to the next-to-leading order. A numerical analysis of the hadronic decay width of the Higgs boson is made in the six-quark model. The next-to-leading order correction is found to be significant, e.g., 30-20% of the leading term for mH of oue interest, mH ? 1 TeV. Application of our scheme to the decay rates of heavy Higgs bosons of other types is also discussed. 相似文献
15.
F. David 《Communications in Mathematical Physics》1981,81(2):149-170
In the two-dimensionalO(N) nonlinear models, the expectation value of anyO(N) invariant observable is shown to have an infrared finite weak coupling perturbative expansion, although it is computed in the wrong spontaneously broken symmetry phase. This result is proved by extracting all infrared divergences of any bare Feynman amplitude atD=2– dimension. The divergences cancel at any order only for invariant observables. The renormalization atD=2 preserves the infrared finiteness of the theory. 相似文献
16.
We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using
the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone
theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one
determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as
the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation,
which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap
equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson
mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach
is also discussed.
Received: 21 June 2000 / Accepted: 13 September 2000 相似文献
17.
We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under renormalization group transformations. The model is used as a playground to investigate various features of field theory at finite temperature. For example we verify that, as expected from general arguments, the cancellation of ultraviolet divergences takes place at finite temperature without the need for introducing counterterms beyond those of zero temperature. As well known, the discrete chiral symmetry of the (1+1)-dimensional model is spontaneously broken at zero temperature and restored, in leading order, at some temperature Tc; we find that the 1/N approximation breaks down for temperatures below Tc: as the temperature increases, the fluctuations become eventually too large to be treated as corrections, and a Landau pole invalidates the calculation of the effective potential in the vicinity of its minimum. Beyond Tc, the 1/N expansion becomes again regular: it predicts that in leading order the system behaves as a free gas of massless fermions and that, at the next-to-leading order, it remains weakly interacting. In the limit of large temperature, the pressure coincides with that given by perturbation theory with a coupling constant defined at a scale of the order of the temperature, as expected from asymptotic freedom. 相似文献
18.
19.
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method. 相似文献
20.
R. Dick A. Pollok-Narayanan H. Steinacker J. Wess 《The European Physical Journal C - Particles and Fields》1999,7(2):363-368
A q–deformed anharmonic oscillator is defined within the framework of q–deformed quantum mechanics. It is shown that the Rayleigh–Schr?dinger perturbation series for the bounded spectrum converges
to exact eigenstates and eigenvalues, for q close to 1. The radius of convergence becomes zero in the undeformed limit.
Received: 6 August 1998 / Published online: 16 September 1998 相似文献