Nuclear effective interactions and spin excitations

In view of the one-boson-exchange model for the nucleon-nucleon interaction and the Hartree-Fock (HF) interaction, we formulate the effective interactions for particle-hole states in terms of the exchange of the fields which are confined in the nucleus. This theory, as an extension to the nuclear field theory (NFT), takes into account the propagation of the fields which is neglected in NFT. The effective interactions thus obtained reproduce the energies of a sequence of electric giant resonances and the core polarizabilities associated with the resonances. It is found that the coupling constants of the σ- and ω-fields are suppressed for the particle-hole interaction by 60% with respect to the HF interaction. As for the effective interactions involving nucleon spins, we consider the fields coupled to nucleon spins. The effective interactions obtained, essentially different from those in NFT, have a tensor component. We analyse the energies and cross sections for excitation of stretched spin particle-hole states which are the most sensitive to the tensor force. The effective interaction responsible for the stretched spin states is shown to be consistent with that for the magnetic resonances observed in the (p, n) reactions.     

Functional approach to nuclear field theory: A schematic model with pairing and particle-hole forces

Path integral techniques in collective variables are applied to a schematic model with monopole pairing and particle-hole forces. The single-particle and collective excitation modes of the system for various kinds of phase transitions are discussed. We formulate a modified perturbation theory (loop expansion) from which, finally, nuclear field theory (NFT) is obtained. The NFT Lagrangian is strictly derived. The graphical rules of the NFT expansion come out automatically.     

Nuclear field theory

By using path integral techniques nuclear field theory (NFT) is developed for Fermi systems interacting via a general two-body force. The NFT Lagrangian is strictly derived. As a by-product, the corresponding graphical rules are obtained. The relation between the NFT and the conventional Feynman diagrammatic many-body perturbation theory is established for processes connecting initial and final states, too.     

Separation of Dirac's Hamiltonian by Van Vleck transformation

ABSTRACT

The now classic Foldy–Wouthuysen transformation (FWT) was introduced as successive unitary transformations. This fundamental idea has become the standard in later developments such as the Douglas–Kroll transformation (DKT) – but it is not the only possibility. FWT can be seen as a simple special case of the general Van Vleck transformation (VVT) which besides the successive version has another, known as the canonical because of a series of nice mathematical properties discovered gradually over time. The aim of the present paper is to compare the two approaches – which give identical results in the lower orders, but not in the higher. After having recapitalised both, we apply them to Dirac's Hamiltonian for the electron in a constant electromagnetic field, written with so few assumptions about the operators that the mathematical techniques stand out separated from the terminology of relativistic quantum mechanics. FWT for a free particle is dealt with by a recent geometric approach to VVT. The original FWT is continued through the next non-zero orders. DKT is considered with special weight on equivalent formulations of the generalised and the optimised forms introduced by Wolf, Reiher and Hess.     

Neurofeedback Training Based on Motor Imagery Strategies Increases EEG Complexity in Elderly Population

Neurofeedback training (NFT) has shown promising results in recent years as a tool to address the effects of age-related cognitive decline in the elderly. Since previous studies have linked reduced complexity of electroencephalography (EEG) signal to the process of cognitive decline, we propose the use of non-linear methods to characterise changes in EEG complexity induced by NFT. In this study, we analyse the pre- and post-training EEG from 11 elderly subjects who performed an NFT based on motor imagery (MI–NFT). Spectral changes were studied using relative power (RP) from classical frequency bands (delta, theta, alpha, and beta), whilst multiscale entropy (MSE) was applied to assess EEG-induced complexity changes. Furthermore, we analysed the subject’s scores from Luria tests performed before and after MI–NFT. We found that MI–NFT induced a power shift towards rapid frequencies, as well as an increase of EEG complexity in all channels, except for C3. These improvements were most evident in frontal channels. Moreover, results from cognitive tests showed significant enhancement in intellectual and memory functions. Therefore, our findings suggest the usefulness of MI–NFT to improve cognitive functions in the elderly and encourage future studies to use MSE as a metric to characterise EEG changes induced by MI–NFT.     

Quantum study of Foldy--Wouthuysen--Tani theory on lattice

We study here a quantum version of Foldy--Wouthuysen--Tani (FWT) transformation and compare the similarities and differences between the quantum and the classic FWT theories. Then the improvement of action on lattice is discussed. The result shows that it is not necessary to improve the covariant difference along the time direction on lattice. Finally we discuss briefly the structure of physical vacuum and give a model independent of field condensate.     

The boson-fermion hybrid representation formulation,I

A boson-fermion hybrid representation is presented. In this framework, a fermion system is described concurrently by the bosonic and the fermionic degrees of freedom. A fermion pair in this representation can be treated as a boson without violating the Pauli principle. Furthermore the “bosonic interactions” are shown to originate from the exchange processes of the fermions and can be calculated from the original fermion interactions. Both the formulation of the BFH representations for the even and odd nuclear systems are given. We find that the basic equation of the nuclear field theory (NFT) is just the usual Schrödinger equation in such a representation with the empirical NFT diagrammatic rules emerging naturally. This theory was numerically checked in the case of four nucleons moving in a single-j shell and the exactness of the theory was established.     

Effective potential for the massless KPZ equation

In previous work we have developed a general method for casting a classical field theory subject to Gaussian noise (that is, a stochastic partial differential equation (SPDE)) into a functional integral formalism that exhibits many of the properties more commonly associated with quantum field theories (QFTs). In particular, we demonstrated how to derive the one-loop effective potential. In this paper we apply the formalism to a specific field theory of considerable interest, the massless KPZ equation (massless noisy Burgers equation), and analyze its behavior in the ultraviolet (short-distance) regime. When this field theory is subject to white noise we can calculate the one-loop effective potential and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet renormalizable in higher dimensions. We show that the one-loop effective potential for the massless KPZ equation is closely related to that for λφ⁴ QFT. In particular, we prove that the massless KPZ equation exhibits one-loop dynamical symmetry breaking (via an analog of the Coleman–Weinberg mechanism) in 1 and 2 space dimensions, and that this behavior does not persist in 3 space dimensions.     

A convergence study of Dyson's boson expansion for weak coupling situations in 209Bi

In this paper we study within the Dyson boson expansion (DBE) the particle-vibration coupling in ²⁰⁹Bi as a function of the number of configurations one is taking into account (vertical convergence). We find that the energies converge quite rapidly but that it is somewhat more difficult to achieve convergence also for the transition probabilities. We essentially investigate the well-known septuplet and decuplet in ²⁰⁹Bi and find reasonable agreement with experiment.     

Generally covariant quantum field theory and scaling limits

The formulation of a generally covariant quantum field theory is described. It demands the elimination of global features and a characterization of the theory in terms of the allowed germs of families of states. A simple application is the computation of counting rates of accelerated idealized detectors. As a first orientation we discuss here the consequences of the assumption that the states have a short distance scaling limit. The scaling limit at a point gives a reduction of the theory to tangent space. It contains kinematical information but not the full dynamical laws. The reduced theory will, under rather general conditions, be invariant under translations and under a proper subgroup of the linear transformations in tangent space. One interesting possibility is that it is invariant under SLR(4). Then the macroscopic metric must evolve as a cooperative effect in finite size regions. The other natural possibility is that each family (coherent folium) of states defines a microscopic metric by the scaling limit and the tangent space theory reduces to a theory of free massless fields in a Minkowski space. Irrespective of the assumption of a scaling limit we show that the theory can be constructed from strictly local information.     

Quantum Versus Stochastic Processes and the Role of Complex Numbers

We argue that the complex numbers are an irreducible object of quantum probability: this can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having the complex phases as primitive ingredient implies that we need to accept nonadditive probabilities. This has the desirable consequence of removing constraints of standard theorems about the possibility of describing quantum theory with commutative variables. Motivated by the formalism of consistent histories and keeping an analogy with the theory of stochastic processes, we develop a (statistical) theory of quantum processes: they are characterized by the introduction of a density matrix on phase space paths (it thus includes phase information) and fully reproduces quantum mechanical predictions. We can write quantum differential equations (in analogy to Langevin equation) that could be interpreted as referring to individual quantum systems. We describe the reconstruction theorem by which a quantum process can yield the standard Hilbert space structure if the Markov property is imposed. We discuss the relevance of our results for the interpretation of quantum theory (a sample space is possible if probabilities are nonadditive) and quantum gravity (the Hilbert space arises here after the consideration of a background causal structure).     

The IR stability of de Sitter QFT: physical initial conditions

This work uses Lorentz-signature in-in perturbation theory to analyze the late-time behavior of correlators in time-dependent interacting massive scalar field theory in de Sitter space. We study a scenario recently considered by Krotov and Polyakov in which the coupling g turns on smoothly at finite time, starting from g = 0 in the far past where the state is taken to be the (free) Bunch–Davies vacuum. Our main result is that the resulting correlators (which we compute at the one-loop level) approach those of the interacting Hartle–Hawking state at late times. We argue that similar results should hold for other physically-motivated choices of initial conditions. This behavior is to be expected from recent quantum “no hair” theorems for interacting massive scalar field theory in de Sitter space which established similar results to all orders in perturbation theory for a dense set of states in the Hilbert space. Our current work (1) indicates that physically motivated initial conditions lie in this dense set, (2) provides a Lorentz-signature counter-part to the Euclidean techniques used to prove such theorems, and (3) provides an explicit example of the relevant renormalization techniques.     

Observations on the moduli space of superconformal field theories

Some aspects of the moduli space of superconformal field theories are discussed. It is helpful to consider the conformal field theory as a background for propagation of strings and to exploit the space-time interpretation. Using this point of view we show that the metric on the moduli space of N = 4 superconformal field theory with c = 6 is locally that of O(20,4)/O(20) × O(4). We also discover some properties of the moduli space of N = 2 superconformal field theories with c = 9. Particular examples of these conformal field theories are sigma models on four- and six-dimensional Calabi-Yau spaces. Therefore, we can use this technique to learn about the moduli space of these spaces. For c = 6 we recover the known moduli space of K₃. Our analysis of the c = 9 system leads to a new coupling in four dimensional supergravity. As a by-product, we prove that gauge couplings cannot depend on the moduli of N = 1 space-time supersymmetric compactifications.     

A Relativistic Gauge Theory of Nonlinear Quantum Mechanics and Newtonian Gravity

A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schrödinger picture of a given field theory. While, for simplicity, we study the example of a \(\mathcal{U}(1)\) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, similar to recently studied Schrödinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. A probabilistic interpretation (Born’s rule) holds, provided the underlying model is scale free.     

Degenerate band edges in optical fiber with multiple grating: efficient coupling to slow light

Degenerate band edges (DBEs) of a photonic bandgap have the form (ω-ω(D)) ∝k(2m) for integers m>1, with ω(D) the frequency at the band edge. We show theoretically that DBEs lead to efficient coupling into slow-light modes without a transition region, and that the field strength in the slow mode can far exceed that in the incoming medium. A method is proposed to create a DBE of arbitrary order m by coupling m optical modes with multiple superimposed gratings. The enhanced coupling near a DBE occurs because of the presence of one or more evanescent modes, which are absent at conventional quadratic band edges. We furthermore show that the coupling can be increased or suppressed by varying the number of excited evanescent waves.     

Lattice gauge theories and motion in group space

We extend the SU(2) lattice gauge theory of Kogut and Susskind to a general non-Abelian gauge group. At the Lagrangian level, we find the theory to be related to the motion of a point in group space. We then quantise such a system using the natural geometric structure of group parameter space, and we apply our results to find the Hamiltonian for the general lattice gauge theory. We also discuss the large N behaviour of the theory.     

Non-minimally coupled scalar fields, Holst action and black hole mechanics

The paper deals with the extension of the Weak Isolated Horizon (WIH) formulation of black hole horizons to the non-minimally coupled scalar fields. In the early part of the paper, we introduce an appropriate Holst type action to incorporate scalar fields non-minimally coupled to gravity and construct the covariant phase space of the theory. Using this phase space, we proceed to prove the laws of black hole mechanics. Further, we show that with a gauge fixing, the symplectic structure on the horizon reduces to that of a U(1) Chern–Simons theory. The level of the Chern–Simons theory is shown to depend on the non-minimally coupled scalar field.     

Structural Properties of Anthracene Under High Pressure

The aim of our studies is to investigate the nature of intermolecular interactions in crystals based on aromatic molecules. For this purpose we carry out angle dispersive (ADXD) as well as energy dispersive (EDXD) X-ray diffraction experiments under pressure in combination with Rietveld refinement. The other approach is density functional theory (DFT), where our calculations are based on the experimentally obtained lattice parameters. In the present work we focus on anthracene C 14 H 10 (monoclinic space group P2 1 /a) as a representative for the herringbone structure that is common for rigid rod-like molecules. We discuss its structural properties as a function of pressure and find very good agreement between experiment and theory.