The impedance function of a confined polaron and bipolaron: The single-path-integral approach

We use the single-path-integral to calculate the impedance function of the polaron and bipolaron in quantum confinement with the presence of the external fields. The expectation values of the classical equation of motion is considered in order to obtain the impedance function. The mobility of the polaron and bipolaron in quantum confinement is also calculated in the direction parallel and perpendicular to the magnetic field. Without trapping, we also calculate the effective mass of the bipolaron in the magnetic field.     

Particle Creation in the Effective Action Method

The effect of particle creation by nonstationary external fields is considered as a radiation effect in the expectation-value spacetime. The energy of created massless particles is calculated as the vacuum contribution in the energy-momentum tensor of the expectation value of the metric. The calculation is carried out for an arbitrary quantum field coupled to all external fields entering the general second-order equation. The result is obtained as a functional of the external fields. The paper gives a systematic derivation of this result on the basis of the nonlocal effective action. Although the derivation is quite involved and touches on many aspects of the theory, the result itself is remarkably simple. It brings the quantum problem of particle creation to the level of complexity of the classical radiation problem. For external fields like the electromagnetic or gravitational field there appears a quantity, the radiation moment, that governs both the classical radiation of waves and the quantum particle production. The vacuum radiation of an electrically charged source is considered as an example. The research is aimed at the problem of backreaction of the vacuum radiation.     

The interaction of a quantum mechanical oscillator with gravitational radiation

Within the framework of the linearized field equations of gravitation, the interaction operators between a quantum mechanical system and an external gravitational field are derived from the general-covariant Klein-Gordon and Dirac equation. In the case of linearly polarized plane gravitational waves the transition probabilities for absorption and induced and spontaneous emission of gravitational radiation by a quantum mechanical harmonic oscillator are calculated with the help of the time-dependent perturbation method. The results coincide with the classical ones according to the correspondence principle.     

Hadronic spectrum of a holographic dual of QCD

We compute the spectrum of light hadrons in a holographic dual of QCD defined on AdS5 x S5 which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron's valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale Lambda(QCD), is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio of delta to nucleon trajectories is determined by the ratio of zeros of Bessel functions.     

The Arrow of Time in the Equations of Motion

It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an arrow of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized.     

On the general covariance and strong equivalence principles in quantum general relativity

The various physical aspects of the general relativistic principles of covariance and strong equivalence are discussed, and their mathematical formulations are analyzed. All these aspects are shown to be present in classical general relativity, although no contemporary formulation of canonical or covariant quantum gravity has succeeded to incorporate them all. This has, in part, motivated the recent introduction of a geometro-stochastic framework for quantum general relativity, in which the classical frame bundles that underlie the formulation of parallel transport in classical general relativity are replaced by quantum frame bundles. It is shown that quantum frames can take over the role played by complete sets of observables in conventional quantum theory, so that they can mediate the natural transference of the general covariance and the strong equivalence principles from the classical to the quantum general relativistic regime. This results in a geometrostochastic mode of quantum propagation in general relativistic quantum bundles, which is mathematically implemented by path integration methods based on parallel transport along horizontal lifts of geodesics for the vacuum expectation values of a quantum gravitational field in a quantum spacetime supermanifold. The covariance features of this field are embedded in a quantum gravitational supergroup, which incorporates Poincaré as well as diffeomorphism invariance, and resolves the issue of time in quantum gravity.     

Post-post-Newtonian equations of motion for point particles in the general theory of relativity

The post-post-Newtonian equations of motion for point particles are derived from the Einstein gravitational field equations by using the Einstein-Infeld-Hoffmann method with the help of the energy-momentum tensor proposed by Infeld and Plebanski [5, 6]. The obtained equations of motion coincide with the equations derived by Kopeikin [10] by using the Fock method.     

The parity operator in quantum optical metrology

Photon number states are assigned a parity of +1 if their photon number is even and a parity of ?1 if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenberg limit sensitivities are expected to eventually play an important role in attempts to detect gravitational waves in interferometric detection systems such as LIGO and VIRGO.     

Hypothesis of Quark Binding by Condensation of Gluons in Hadrons

Hypothesis of quark binding through condensation of gluons inside hadrons is formulated in the context of a renormalization group procedure for effective particles (RGPEP) in the light-front (LF) Hamiltonian approach to QCD. At the momentum scales of relative motion of hadronic constituents that are comparable with Λ _QCD , the hypothetical boost-invariant constituent dynamics is identified using gauge symmetry. The resulting picture of mesons and baryons closely resembles constituent quark models with harmonic oscillator potentials, shares some features of AdS/QCD, and can be systematically studied using RGPEP in QCD.     

Exact treatment of the Jaynes–Cummings model under the action of an external classical field

We consider the usual Jaynes–Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency ω₀ and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity.     

AdS/QCD and Applications of Light-Front Holography

Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter(AdS) space and frame-independent light-front wavefunctions of hadrons in(3 + 1)-dimensional physical space-time,thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD,a useful framework which describes the correspondence between theories in a modified AdS 5 background and confining field theories in physical space-time.To a first semiclassical approximation,where quantum loops and quark masses are not included,this approach leads to a single-variable light-front Schro¨dinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum.The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time.The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.We give an overview of the light-front holographic approach to strongly coupled QCD.In particular,we study the photon-to-meson transition form factors(TFFs) FMγ(Q 2) for γ→ M using light-front holographic methods.The results for the TFFs for the η and η ' mesons are also presented.Some novel features of QCD are discussed,including the consequences of confinement for quark and gluon condensates.A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.     

A curiosity concerning the role of coherent states in quantum field theory

In the usual Fock quantisation of fields in Minkowski space-time, one has the result that the expectation value of the quantum Hamiltonian in any coherent state equals the energy of the classical field at which the state is peaked. It is shown that this property can be used tocharacterise the usual Fock representation. It is also pointed out that the entire analysis goes through for a substantially more general class of systems including, in particular, Bose fields in arbitrary stationary space-times.     

Induced rotation in the Papapetrou equations

We obtain an integral form of the Papapetrou equations, which describes the motion of an extended body in an external gravitational field. Using the Fock method, we calculate an explicit form for the components of the spin tensor and derive relativistic equations of rotational motion in the Schwarzschild space V₄. We show that the spin of the body becomes proportional not only to the angular velocity but also to the angular momentum. Thus, induced rotation also follows from the Papapetrou equations.Astrophysics Institute, Kazan Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 117–124, October, 1992.     

A self-consistent approach to quantum field theory for extended particles

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis.Supported in part by an NSERC grant.     

SYNTHESIS OF PERTURBATIVE AND NONPERTURBATIVE QUANTUM CHROMODYNAMICS

Hadronic structure in QCD has been analyzed by using the Fock state wavefunctions of hadrons defined by quantizing quantum chromodynaraics at equal time of the light-cone. They provide a unified approach to QCD phenomenology. We have presented a convenient method for operator product expansion in the external background fields and have obtained the distributior: amplitude moments values from QCD sum rule by introdution the condensate effect of quarks and gluons. These results are in agreement with the present data.     

Cutoff anti-de Sitter space/conformal-field-theory duality and the quest for braneworld black holes

Significant evidence is presented in favor of the holographic conjecture that "4D black holes localized on the brane found by solving the classical bulk equations in AdS5 are quantum corrected black holes and not classical ones." The quantum correction to the Newtonian potential is computed using a numerical computation of in Schwarzschild spacetime for matter fields in the zero-temperature Boulware vacuum state. For the conformally invariant scalar field the leading order term is equivalent to that previously obtained in the weak-field approximation using Feynman diagrams and which has been shown to be equivalent, via the anti-de Sitter space/conformal-field-theory (AdS/CFT) duality, to the analogous calculation in Randall-Sundrum braneworlds. The 4D backreaction equations are used to make a prediction about the existence and the possible spacetime structure of macroscopic static braneworld black holes.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.