Schwinger algebra for quaternionic quantum mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states N→∞.     

G-essence with Yukawa interactions

We study the g-essence model with Yukawa interactions between a scalar field φ and a Dirac field ψ. For the homogeneous, isotropic and flat Friedmann–Robertson–Walker universe filled with the such g-essence, the exact solution of the model is found. Moreover, we reconstruct the corresponding scalar and fermionic potentials which describe the coupled dynamics of the scalar and fermionic fields. It is shown that some particular g-essence models with Yukawa interactions correspond to the usual and generalized Chaplygin gas unified models of dark energy and dark matter. Also we present some scalar–fermionic Dirac–Born–Infeld models corresponding g-essence models with Yukawa interactions which again describe the unified dark energy–dark matter system.     

Feynman propagator for spin foam quantum gravity

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".     

Extended electron and nonlocal electromagnetic interaction: The perturbation theory

The nonlocal interaction between electrons and electromagnetic fields is considered. It is shown that different contraction forms of interacting fields are equivalent to different nonlocal theories where nonlocality is connected to either the photon field or the electron field, or to both these fields simultaneously. The nonlocal theory where the electron carries nonlocality is studied in detail. The gauge invariance of this model is achieved by using thed-operation applying the perturbation theory. Primitive Feynman diagrams of the nonlocal theory are investigated and a restriction on the “size”l of the electron is obtained. From low-energy experimental data from tests of local quantum electrodynamics it follows thatl≦10⁻¹⁵ cm.     

Anisotropic negative magnetoresistance in one-dimensional channels of porous silicon

It is found that the magnetoresistance of manganese-doped porous amorphous silicon in fields 0–5 T is negative and depends on the orientation of the magnetic field. The experimental curves of the magnetic-field dependence are described well by the theory of quantum corrections to the conductivity in the one-dimensional case. The phase coherence length in the material is ≈25 nm at T=4.2 K. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 189–193 (10 February 1999)     

Braneworld model of dark matter: structure formation

Following a previous work (García-Aspeitia in Gen Rel Grav 43:315–329, 2011), we further study the behavior of a real scalar field in a hidden brane in a configuration of two branes embedded in a five dimensional bulk. We find an expression for the equation of state for this scalar field in the visible brane in terms of the fields of the hidden one. Additionally, we investigated the perturbations produced by this scalar field in the visible brane with the aim to study their dynamical properties. Our results show that if the kinetic energy of the scalar field dominates during the early universe the perturbed scalar field could mimic the observed dynamics for the dark matter in the standard paradigm. Thus, the scalar field dark matter hypothesis in the context of braneworld theory could be an interesting alternative to the nature of dark matter in the Universe.     

Projective Invariance in Cosmological Models and Dark Energy

We study theories of gravitation that are based on the Einstein – Hilbert action that are not projectively invariant and can therefore completely determine their connections. We are thus lead to the conclusion that the geometry is necessarily Riemann – Cartan and at least the trace part of a torsion field must be present. We examine the consequence of including these torsion fields in cosmological models. Our results differ from those obtained earlier in the Einstein – Cartan – Sciama – Kibble theory. We also consider a model that includes a series of quadratic torsion terms. This series leads to a potential function that has the effect of “turning on” the cosmological constant. This potential function then acts like dark energy. This model also shows that the torsion field can produce an inflationary period. PACS: 04.02 Cv, 95.30 Sf, 98.80-k     

On the gravitodynamics of moving bodies

In the present work we propose a generalization of Newton’s gravitational theory from the original works of Heaviside and Sciama, that takes into account both approaches, and accomplishes the same result in a simpler way than the standard cosmological approach. The established formulation describes the local gravitational field related to the observables and effectively implements the Mach’s principle in a quantitative form that retakes Dirac’s large number hypothesis. As a consequence of the equivalence principle and the application of this formulation to the observable universe, we obtain, as an immediate result, a value of Ω = 2. We construct a dynamic model for a galaxy without dark matter, which fits well with recent observational data, in terms of a variable effective inertial mass that reflects the present dynamic state of the universe and that replicates from first principles, the phenomenology proposed in MOND. The remarkable aspect of these results is the connection of the effect dubbed dark matter with the dark energy field, which makes it possible for us to interpret it as longitudinal gravitational waves.     

On the Origin of Entropic Gravity and Inertia

It was recently suggested that quantum field theory is not fundamental but emerges from the loss of phase space information about matter crossing causal horizons. Possible connections between this formalism and Verlinde’s entropic gravity and Jacobson’s thermodynamic gravity are proposed. The holographic screen in Verlinde’s formalism can be identified as local Rindler horizons and its entropy as that of the bulk fields beyond the horizons. This naturally resolves some issues on entropic gravity. The quantum fluctuation of the fields is the origin of the thermodynamic nature of entropic gravity. It is also suggested that inertia is related to dragging Rindler horizons.     

Does antimatter emit a new light?

Contemporary theories of antimatter have a number of insufficiencies which stimulated the recent construction of the new isodual theory based on a certain anti-isomorphic map of all (classical and quantum) formulations of matter called isoduality. In this note we show that the isodual theory predicts that antimatter emits a new light, called isodual light, which can be distinguished from the ordinary light emitted by matter via gravitational interactions (only). In particular, the isodual theory predicts that all stable antiparticles such as the isodual photon, the positron and the antiproton experience antigravity in the field of matter (defined as the reversal of the sign of the curvature tensor). The antihydrogen atom is therefore predicted to: experience antigravity in the field of Earth; emit the isodual photon; and have the same spectroscopy of the hydrogen atom, although subjected to an anti-isomorphic isodual map. In this note we also show that the isodual theory predicts that bound states of elementary particles and antiparticles (such as the positronium) experience ordinary gravitation in both fields of matter and antimatter, thus bypassing known objections against antigravity. A number of intriguing and fundamental, open theoretical and experimental problems of “the new physics of antimatter” are pointed out. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Theory of (Exclusively) Local Beables

It is shown how, starting with the de Broglie–Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot-wave” field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear—i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research.     

Making the Case for Conformal Gravity

We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever. With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by ’t Hooft in which a connection between conformal gravity and Einstein gravity has been found.     

Perturbative approach to the hydrogen atom in a strong magnetic field

We consider states of the hydrogen atom with the principal quantum number n≤3 and zero magnetic quantum number in a constant homogeneous magnetic field ?. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n³?/?₀～5, where ?₀ is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.     

Renormalization of a quantum field theory model in a curved space-time with torsion

A quantum field theory model that contains interacting non-Abelian gauge fields, scalar fields, and spinor fields is considered in a curved space-time with torsion. The cone-loop counterterms are found. It is shown that the multiplicative renormalization condition requires a nonminimal coupling of the matter with the gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 94–100, August, 1985.     

Automatic Regularization by Quantization in Reducible Representations of CCR: Point-Form Quantum Optics with Classical Sources

Electromagnetic fields are quantized in a manifestly covariant way by means of a class of reducible “center-of-mass N-representations” of the algebra of canonical commutation relations (CCR). The four-potential A _a (x) transforms in these representations as a Hermitian four-vector field in Minkowski four-position space (without change of gauge), but in momentum space it splits into spin-1 massless photons and two massless scalars. What we call quantum optics is the spin-1 sector of the theory. The scalar fields have physical status similar to that of dark matter (spin-1 and spin-0 particle numbers are separately conserved). There are no negative-norm or zero-norm states. Unitary dynamics is given by the point-form interaction picture, with minimal-coupling Hamiltonian constructed from fields that are free on the null-cone boundary of the Milne universe. SL(2,C) transformations as well as the dynamics are represented unitarily in the Hilbert space corresponding to N four-dimensional oscillators. Vacuum is a Bose-Einstein condensate of the N-oscillator gas and is given by any N-oscillator product state annihilated by all annihilation operators. The form of A _a (x) is determined by an analogue of the twistor equation. The same equation guarantees that the set of vacuum states is Poincaré invariant. The formalism is tested on quantum fields produced by pointlike classical sources. Photon statistics is well defined even for pointlike charges, with ultraviolet and infrared regularizations occurring automatically as a consequence of the formalism. The probabilities are not Poissonian but of a Rényi type with α=1−1/N; the Shannon limit N→∞ is an ultraviolet/infrared-regularized Poisson distribution. The average number of photons occurring in Bremsstrahlung splits into two parts: The one due to acceleration, and the one that remains nonvanishing even for inertially moving charges. Classical Maxwell electrodynamics is reconstructed from coherent-state averaged solutions of Heisenberg equations. We show in particular that static pointlike charges polarize vacuum and produce effective charge densities and fields whose form is sensitive to both the choice of representation of CCR and the corresponding vacuum state.     

A Spin-Statistics Theorem for Quantum Fields¶on Curved Spacetime Manifolds¶in a Generally Covariant Framework

A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum field theory is an assignment of quantum fields to globally hyperbolic spacetimes with spin-structure where each quantum field propagates on the spacetime to which it is assigned. Imposing very natural conditions such as local general covariance, existence of a causal dynamical law, fixed spinor- or tensor type for all quantum fields of the theory, and that the quantum field on Minkowski spacetime satisfies the usual conditions, it will be shown that a spin-statistics theorem holds: If for some of the spacetimes the corresponding quantum field obeys the “wrong” connection between spin and statistics, then all quantum fields of the theory, on each spacetime, are trivial. Received: 1 March 2001 / Accepted: 28 May 2001     

Dark matter in quantum gravity

We show that quantum gravity, whatever its ultra-violet completion might be, could account for dark matter. Indeed, besides the massless gravitational field recently observed in the form of gravitational waves, the spectrum of quantum gravity contains two massive fields respectively of spin 2 and spin 0. If these fields are long-lived, they could easily account for dark matter. In that case, dark matter would be very light and only gravitationally coupled to the standard model particles.     

Point Interactions in One Dimension and Holonomic Quantum Fields

We introduce and study a family of quantum fields, associated to δ-interactions in one dimension. These fields are analogous to holonomic quantum fields of Sato et al. in Holonomic quantum fields I–V (Publ. RIMS, Kyoto University, 14: 223–267, 1978; 15: 201–278, 1979; 15: 577–629, 1979; 15: 871-972, 1979; 16: 531–584, 1979). Corresponding field operators belong to an infinite-dimensional representation of the group in the Fock space of ordinary harmonic oscillator. We compute form factors of such fields and their correlation functions, which are related to the determinants of Schroedinger operators with a finite number of point interactions. It is also shown that these determinants coincide with tau functions, obtained through the trivialization of the det^*-bundle over a Grassmannian associated to a family of Schroedinger operators.     

Interacting Entropy-Corrected Holographic Chaplygin Gas Model

Holographic dark energy (HDE), presents a dynamical view of dark energy which is consistent with the observational data and has a solid theoretical background. Its definition follows from the entropy-area relation S(A), where S and A are entropy and area respectively. In the framework of loop quantum gravity, a modified definition of HDE called “entropy-corrected holographic dark energy” (ECHDE) has been proposed recently to explain dark energy with the help of quantum corrections to the entropy-area relation. Using this new definition, we establish a correspondence between modified variable Chaplygin gas, new modified Chaplygin gas and the viscous generalized Chaplygin gas with the entropy corrected holographic dark energy and reconstruct the corresponding scalar potentials which describe the dynamics of the scalar field.     

The Effects of Tachyonic and Phantom Fields in the Intermediate and Logamediate Scenarios of the Anisotropic Universe

In this work, we have analyzed two scenarios namely, “intermediate” and “logamadiate” scenarios for closed, open and flat anisotropic universe in presence of phantom field, normal tachyonic field and phantom tachyonic field. We have assumed that there is no interaction between the above mentioned dark energy and dark matter. In these two types of the scenarios of the Universe, the nature of the scalar fields and corresponding potentials have been investigated. In intermediate scenario, (i) the potential for normal tachyonic field decreases, (ii) the potentials for phantom tachyonic field and phantom field increase with the corresponding fields. Also in logamediate scenario, (i) the potential for normal tachyonic field increases, (ii) the potentials for phantom tachyonic field and phantom field decrease with the corresponding fields.