On the equivalence principle in quantum theory

The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is capable of covering quantum phenomena too, will be proposed. It is shown that this generalised equivalence principle is valid for matter wave interferometry and for the dynamics of expectation values. In addition, the use of this equivalence principle makes it possible to determine the structure of the interaction of quantum systems with gravitational and inertial fields. It is also shown that the path of the mean value of the position operator in the case of gravitational interaction does fulfill this generalised equivalence principle.     

On the equivalence between the Wess-Zumino action and the free Fermi theory in two dimensions

Using the functional technique we prove the bosonization rules of Witten for the currents in a non-abelian two-dimensional theory with a particular regularization of the Fermi theory.     

The exciton-polariton: Microscopic derivation of the phenomenological theory

From a microscopic model including all excitonic levels, we derive the exciton-polariton dispersion spectrum. Our results, which differ from previous microscopic calculations, justify the phenomenological theory in which only the lowest exciton level is considered. We show how the higher levels generate the phenomenological “high frequency dielectric constant” which not only modifies the photon velocity at q 0, but also reduces the exciton-photon coupling.     

On the equivalence of the two most favoured Calabi-Yau compactifications

We discuss the two known multiply connected Calabi-Yau manifolds which give rise to three generations of elementary particles when chosen as the classical vacuum configuration of theE ₈×E ₈ heterotic superstring. It is shown that these two manifolds are diffeomorphic.Part of this work carried out at and supported by the IBM T.J. Watson Research Center, Yorktown Heights, NYOn leave from Lyman Laboratory of Physics, Harvard University     

On the equivalence of the Euclidean and Wightman formulation of field theory

A mistake in the paper [1] on the “Axioms for Euclidean Green's Functions” is corrected in the following sense: thanks to these axioms the Euclidean Schwinger functionsS _n can be analytically continued to the corresponding Wightman functionsW _n possessing all the correct analyticity properties and satisfying a generalized positivity condition in the complex domain. It is however suggested by the proof that their tempered behaviour near the Minkowski points cannot be guaranteed without additional assumptions.     

Quantum theory of sticking: equivalence of various approaches and application to a simple model

The basic formulae of four different quantum mechanical approaches to the calculation of the sticking coefficient of an atom on a cold solid are re-examined in order to discuss the connections between them. All approaches pursued exactly give the same result, and this is exhibited for a one-dimensional model which is exactly solvable to provide closed-form formulae for the sticking coefficient. Numerical results, which reproduce the qualitative behaviour of atomic sticking, are presented for different assumed densities of substrate excitations responsible for the energy loss, including the physically important cases of low-energy single phonons, and low-energy electron-hole pairs in a metal.     

On the equivalence of the Fröhlich and the Bloch approaches to the electron-phonon coupling

It is shown that the Fröhlich approach for calculating electron-phonon coupling constants based on wave functions moving with the vibrating atoms can be set on a rigorous basis. This approach and the Bloch approach are shown to lead to the same physical results provided that one stays within the adiabatic approximation and considers both first and second order vertices (in the harmonic approximation). Advantages of the Fröhlich approach in past and in possible future calculations are discussed.     

On thermodynamic approaches to conformal field theory

We present the thermodynamic Bethe ansatz as a way to factorize the partition function of a 2d field theory, in particular, a conformal field theory and we compare it with another approach to factorization due to Schoutens which consists of diagonalizing matrix recursion relations between the partition functions at consecutive levels. We prove that both are equivalent, taking as examples the SU(2) spinons and the 3-state Potts model. In the latter case we see that there are two different thermodynamic Bethe ansatz equation systems with the same physical content, of which the second is new and corresponds to a one-quasiparticle representation, as opposed to the usual two-quasiparticle representation. This new thermodynamic Bethe ansatz system leads to a new dilogarithmic formula for the central charge of that model.     

On the equivalence of standard and covariant perturbation series in non-polynomial pion lagrangian field theory

Recently a covariant perturbation approach has been developed to give a perturbation expansion of the chiral-invariant pion theory which does not depend on the choice of pion coordinates. We prove that this covariant approach is equivalent to standard perturbation theory. Our method explicitly shows how one can express covariant graphs by contributions of non-covariant ones and vice versa. We neglect contributions vanishing on the mass shell.     

On the two methods of kinetic theory of ECRM

The kinetic theory based on the expansion of local field in the guiding center coordinate system, presented by paper[1]–[3], has successfully developed into a theoretical system. The mathematical background and physical explanation of setting up the guiding center coordinate system is expounded in the paper. By using the methods of the guiding center and waveguide coordinate systems respectively, the same dispersion equations for interaction of an axially symmetrical single momentum electron beam with TE_mn field in the circular waveguide are rigorously derived. A number of mistakes in paper[4] are indicated as well.     

Self-trapping phenomenon in exciton-polariton dynamics

The polariton dynamics in a microcavity in the parametric oscillator mode, when two pump polaritons are transformed into signal and idler polaritons and vice versa, has been studied. A nonlinear differential equation is obtained, which describes the temporal evolution of pump-polariton density, the solution of which is expressed in terms of the Jacobi elliptical functions. The amplitude and period of polaritondensity oscillations are determined by the initial polariton densities and the resonance detuning. The possibility of self-trapping in exciton-polariton dynamics is predicted.     

Note on the equivalence of different approximations in the relaxation theory

We briefly discuss relations between different variants of the second order generalized master equations (GME), in particular among different types of the Markov-Born approximation of time-convolution GME and Born approximation in time-convolutionless one. We prove that equivalence valid in the van Hove limit does not in general apply for other types of scaling. On the other hand, for other scalings one appropriate form of the interaction representation always exist that reproduces this equivalence known from the weak-coupling (van Hove) one.     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

On the two approaches to the data analysis of the Cassini interplanetary relativity experiment

We compare two theoretical approaches to the data analysis of the Cassini relativity experiment based on the Doppler tracking and the time delay technique that were published correspondingly by Kopeikin et al. [S.M. Kopeikin, A.G. Polnarev, G. Schäfer, I.Yu. Vlasov, Phys. Lett. A 367 (2007) 276] and by Bertotti et al. [B. Bertotti, N. Ashby, L. Iess, Class. Quantum Grav. 25 (2008) 045013]. Bertotti et al. believed that they found a discrepancy with our paper and claimed that our analysis was erroneous. The present Letter elucidates, however, that the discrepancy is illusory and does not exist. The two techniques give the same result making it evident that the numerical value of the PPN parameter γ measured in the Cassini experiment is indeed affected by the orbital motion of the Sun around the barycenter of the solar system.