DIRAC SEA EFFECTS IN A LINEAR σ MODEL WITH VECTOR AND AXIAL VECTOR FIELDS

1995 ◽  
Vol 10 (07) ◽  
pp. 963-976
Author(s):  
C. A. DE SOUSA
Keyword(s):  
Vector Fields ◽  
Axial Vector ◽  
Collective Phenomena ◽  
Many Body ◽  
New Approach ◽  
Dirac Sea ◽  
Body Techniques ◽  
Classical Vector

We propose a new approach to collective phenomena in a linear σ model which includes classical vector–isovector and pseudovector–isovector fields. The main purpose is to describe meson modes composed of two ingredients: phenomenological structureless fields and [Formula: see text] excitations of the vacuum. This procedure, performed in the context of many-body techniques, provides a natural renormalization process through the [Formula: see text] excitations.

A new approach to the bienergy and biangle of a moving particle lying in a surface of lorentzian space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Talat Körpınar ◽  
Yasin Ünlütürk
Keyword(s):  
Vector Fields ◽  
Elastic Surface ◽  
Geometrical Characterization ◽  
Lorentzian Space ◽  
New Approach ◽  
Darboux Vector ◽  
Moving Particle ◽  
The Relationship ◽  
Surface Curve

AbstractIn this research, we study bienergy and biangles of moving particles lying on the surface of Lorentzian 3-space by using their energy and angle values. We present the geometrical characterization of bienergy of the particle in Darboux vector fields depending on surface. We also give the relationship between bienergy of the surface curve and bienergy of the elastic surface curve. We conclude the paper by providing bienergy-curve graphics for different cases.

A CHIRALLY SYMMETRIC EFFECTIVE ACTION FOR VECTOR AND AXIAL VECTOR FIELDS IN A GLOBAL COLOR SYMMETRY MODEL OF QCD

1989 ◽  
Vol 04 (07) ◽  
pp. 1681-1733 ◽  
Author(s):  
C. D. ROBERTS ◽  
J. PRASCHIFKA ◽  
R. T. CAHILL
Keyword(s):  
Effective Action ◽  
Bound States ◽  
Vector Fields ◽  
Axial Vector ◽  
Form Factors ◽  
Local Fields ◽  
Local Action ◽  
Massless Fermion ◽  
Yang Mills ◽  
Local Functions

We consider the quantum field theory of a model of an extended Nambu-Jona-Lasinio type with a QCD based nonlocal fermion current-current interaction which has global SU(Nc) symmetry. We obtain an exact bosonization of this model in four Euclidean dimensions using auxiliary bilocal fields and discuss the dynamical breakdown of chiral symmetry in the massless fermion limit. A local field bosonization is obtained by decomposing the bilocal fields in terms of complete orthonormal sets of functions with the expansion coefficients, which are local functions, identified as the local meson fields. Retaining the ground state pseudoscalar, vector and pseudovector local fields we obtain a local effective action for this sector of the theory. The derivative expansion of the fermionic determinant necessary to obtain this local action is self-regularizing because of the bilocal substructure present in the model which is manifest in the form factors that are associated with the local fields. In our local action the value of each coefficient depends critically on the underlying fermionic dynamics through these form factors and the vacuum functions. As a consequence of this the vector and pseudovector fields in the theory are best interpreted as simple fermion-antifermion bound states rather than as massive Yang-Mills fields or exotic composites of the pseudoscalars; interpretations that we find are not in general admitted when models such as the GCM are treated correctly. Identifying then the physical vector and pseudovector fields with the linearly transforming chiral partners introduced by the bosonization, we obtain an effective action for this sector of the meson spectrum which predicts values for the kinematic and dynamic quantities associated with these fields.

scholarly journals Quantum Crystals in Neutron Stars

1974 ◽  
Vol 53 ◽  
pp. 133-150 ◽  
Author(s):  
V. Canuto ◽  
S. M. Chitre
Keyword(s):  
Neutron Star ◽  
Neutron Stars ◽  
Solid Core ◽  
Many Body ◽  
The Core ◽  
Deep Interior ◽  
Body Techniques ◽  
Quantum Crystals ◽  
The Many ◽  
Orderly Arrangement

Using the many-body techniques appropriate for quantum crystals it is shown that the deep interior of a neutron star is most likely an orderly arrangement of neutrons, protons and hyperons forming a solid. It is shown that a liquid or gas arrangement would produce higher energy. If so, a neutron star can be viewed as two solids (crust and core) permeated by a layer of ordinary or (perhaps) superfluid liquid. Astronomical evidence is in favor of such a structure: the sudden jumps in the periods of the Crab and Vela pulsars that differ by a factor of ∼ 102 can be easily explained by the star-quake model. If the Crab is less massive than Vela (i.e., if it is not dense enough to have a solid core), the star-quakes take place in the crust whereas for Vela they occur in the core.

scholarly journals Hubbard-Stratonovich-like Transformations for Few-Body Interactions

2018 ◽  
Vol 175 ◽  
pp. 11012
Author(s):  
Christopher Körber ◽  
Evan Berkowitz ◽  
Thomas Luu
Keyword(s):  
Perturbation Theory ◽  
Great Accuracy ◽  
Quantum Systems ◽  
Collective Phenomena ◽  
Many Body ◽  
Chiral Perturbation ◽  
Body Level ◽  
The Many ◽  
Three Body ◽  
Number Of Particles

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the an-alytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three-and more-body inter-actions, is presented.

Convergence of stochastic algorithms: from the Kushner–Clark theorem to the Lyapounov functional method

1996 ◽  
Vol 28 (04) ◽  
pp. 1072-1094
Author(s):  
Jean-Claude Fort ◽  
Gilles Pagès
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Functional Method ◽  
Stochastic Algorithms ◽  
Smoothness Assumption ◽  
New Approach ◽  
The Mean ◽  
Path Dependent ◽  
Mean Vector ◽  
Theoretical Results

In the first part of this paper a global Kushner–Clark theorem about the convergence of stochastic algorithms is proved: we show that, under some natural assumptions, one can ‘read' from the trajectories of its ODE whether or not an algorithm converges. The classical stochastic optimization results are included in this theorem. In the second part, the above smoothness assumption on the mean vector field of the algorithm is relaxed using a new approach based on a path-dependent Lyapounov functional. Several applications, for non-smooth mean vector fields and/or bounded Lyapounov function settings, are derived. Examples and simulations are provided that illustrate and enlighten the field of application of the theoretical results.

A LCAO-OO Approach to the Calculation of Electronic Properties of Materials

1997 ◽  
Vol 491 ◽  
Author(s):  
P. Pou ◽  
R. Perez ◽  
J. Ortega ◽  
F. Flores
Keyword(s):  
Electronic Properties ◽  
Correlation Energy ◽  
Many Body ◽  
New Approach ◽  
Exchange Correlation ◽  
Orbital Basis ◽  
Properties Of Materials ◽  
Many Body Effects ◽  
Simple Molecules

ABSTRACTWe present a selfconsistent LCAO approach for describing the electronic properties of materials. This method introduces many-body effects by means of a new approach, whereby a local orbital potential is defined by calculating the exchange-correlation energy as a function of the different orbital occupancies. A LCAO-pseudopotential is also introduced, keeping all the calculations within the context of the local orbital basis. We have applied the method to the calculation of simple molecules and crystals, in both cases we find results that confirm the validity of our approach.

MANY-BODY PHYSICS AND SPONTANEOUS SYMMETRY BREAKING

2006 ◽  
Vol 20 (19) ◽  
pp. 2579-2590 ◽  
Author(s):  
SPARTAK T. BELYAEV
Keyword(s):  
Symmetry Breaking ◽  
Density Matrix ◽  
Spontaneous Symmetry Breaking ◽  
Nuclear Structure ◽  
Bose Gas ◽  
Personal Perspective ◽  
Many Body ◽  
New Approach ◽  
Many Body Physics

The idea of spontaneous symmetry breaking in many-body physics from personal perspective (Bose-gas, nuclear structure and a new approach of Generalized Density Matrix).

scholarly journals Conformal invariance and the metrication of the fundamental forces

2016 ◽  
Vol 25 (12) ◽  
pp. 1644003 ◽  
Author(s):  
Philip D. Mannheim
Keyword(s):  
String Theory ◽  
Conformal Invariance ◽  
Vector Fields ◽  
Axial Vector ◽  
Gravitational Theory ◽  
Einstein Gravity ◽  
Conformal Gravity ◽  
Yang Mills ◽  
Standard Picture ◽  
Fundamental Forces

We revisit Weyl’s metrication (geometrization) of electromagnetism. We show that by making Weyl’s proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion, we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang–Mills theories, and achieve a metrication of all the fundamental forces. Only in the gravity sector does our approach differ from the standard picture of fundamental forces, with our approach requiring that standard Einstein gravity be replaced by conformal gravity. We show that quantum conformal gravity is a consistent and unitary quantum gravitational theory, one that, unlike string theory, only requires four spacetime dimensions.

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