Principle Of Gauge Invariance Research Articles

4He(γ,d)dand3He(γ,p)dreactions in nonlocal covariant model

Photonuclear reaction research is of great interest to obtain information about the structure of nuclei. The investigation of structural effects requires certain insights into the reaction mechanisms, that have to be identified on the basis of the fundamental principles of covariance and gauge invariance. The major achievement of the chosen model is the ability to reproduce the cross-section dependence using the minimal necessary set of parameters. We analyze the two-particle disintegration of 3 He nuclei by photons. Our interest was raised by the fact that 3 He is the simplest many-particle system which admits an exact solutions. We also consider the process 4 He(γ , d)d . This process comes at the expense of the quadrupole absorption of γ -rays, while the dipole transition is suppressed. This property is a consequence of the isospin selection as well as the identity of the particles in the final state. Obtained results describe the energy range from threshold (20 MeV) to 140 MeV. Therefore, the model mentioned in the paper has the peculiarity to be valid not only for the low-energy regime, but also for higher energies. Present paper is devoted to determine the roles of different reaction mechanisms and to solve problems above.

Spatial Allocation of Economy as a Fiber Bundle

This paper considers the approach to specification and modeling of transport influence on spatial allocation of economy, which is essentially new for economics. By applying the concept of fiber bundle, a general model of spatial allocation of market with regard to transport costs is developed. Corresponding mathematical formulation of model equilibrium condition and transition dynamics is stated based on the principle of least action and gauge invariance. Further development of obtained theoretical results within the framework is reviewed.

Equations of motion for a classical color particle in external non-Abelian fermionic and bosonic fields

On the basis of principles of gauge and reparametrization invariance of a real-valued Lagrangian, construction of the action describing the dynamics of a classical color-charged particle interacting with background non-Abelian gauge and fermion fields is considered. The cases of the linear and quadratic dependence of a Lagrangian on the background fermion field are discussed. It is shown that, in both cases, there exist an infinite number of interaction terms. From an iteration scheme, examples of construction of the first few currents and sources induced by a moving particle with non-Abelian charge are given. It is shown that these quantities by a suitable choice of parameters exactly reproduce additional currents and sources obtained previously in [1] on the basis of heuristic considerations.

AN ALTERNATIVE VIEW ON THE ELECTROWEAK INTERACTIONS

We discuss an alternative to the Higgs mechanism which leads to gauge invariant masses for the electroweak bosons. The key idea is to reformulate the gauge invariance principle which, instead of being applied as usual at the level of the action, is applied at the level of the quantum fields. In other words, we define gauge invariant quantum fields which are used to build the action. In that framework, the Higgs field is not necessarily a physical degree of freedom but can merely be a dressing field that does not propagate. If the Higgs boson is not propagating, the weak interactions must become strongly coupled below 1 TeV and have a nontrivial fixed point and would thus be renormalizable at the nonperturbative level. On the other hand, if a gauge invariant Higgs boson is introduced in the model, its couplings to the fermions and the electroweak bosons can be quite different from those expected in the Standard Model.

Theoretical princi les of constructing the equations of motion for a spin color-charged particle in gauge and fermion fields

Based on the most general principles of materiality, gauge, and re-parameterized invariance, the problem of constructing an action describing the dynamics of a classical color-charged particle moving in external non-Abelian gauge and fermion fields is considered. The case of a linear Lagrangian dependence on the external fermion fields is discussed. Within the framework of the description of the color degree of freedom of the particle with half-integer spin by the Grassmann color charges, a new concept of the Grassmann color source of the particle being a fermion analog of the conventional color current is introduced.

Gauge field theory of chirally folded homopolymers with applications to folded proteins

We combine the principle of gauge invariance with extrinsic string geometry to develop a lattice model that can be employed to theoretically describe properties of chiral, unbranched homopolymers. We find that in its low temperature phase the model is in the same universality class with proteins that are deposited in the Protein Data Bank, in the sense of the compactness index. We apply the model to analyze various statistical aspects of folded proteins. Curiously we find that it can produce results that are a very good good match to the data in the Protein Data Bank.

The equations of motion for a classical color particle in background non-Abelian bosonic and fermionic fields

Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and fermion fields is considered. The cases of the linear and quadratic dependence of a Lagrangian on background Grassmann fermion field are discussed. It is shown that in both cases in general there exists an infinite number of interaction terms, which should be included in the Lagrangian in question. Employing a simple iteration scheme, examples of the construction of the first few gauge-covariant currents and sources induced by a moving particle with non-Abelian charge are given. It is found that these quantities, by a suitable choice of parameters, exactly reproduce additional currents and sources previously obtained in Markov and Markova (2007 Nucl. Phys. A 784 443) on the basis of heuristic considerations.

The principle of locality: Effectiveness, fate, and challenges

The special theory of relativity and quantum mechanics merge in the key principle of quantum field theory, the principle of locality. We review some examples of its “unreasonable effectiveness” in giving rise to most of the conceptual and structural frame of quantum field theory, especially in the absence of massless particles. This effectiveness shows up best in the formulation of quantum field theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of global gauge invariance, through the analysis of superselection structure and statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the principle of local gauge invariance. This problem emerges also if one attempts to figure out the fate of the principle of locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localization of events, of the notion of space-time, shows that, in the small, the latter must loose any meaning as a classical pseudo-Riemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the geometry of a basic model of quantum space-time and some attempts to formulate interaction of quantum fields on quantum space-time. The principle of locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely, a principle where the general theory of relativity and quantum mechanics merge, which reduces to the principle of locality at larger scales. Besides exploring its fate, many challenges for the principle of locality remain; among them, the analysis of superselection structure and statistics also in the presence of massless particles, and to give a precise mathematical formulation to the measurement process in local and relativistic terms; for which we outline a qualitative scenario which avoids the Einstein, Podolski, and Rosen paradox.

Dependence of physical interpretations on the choice of electromagnetic gauge

The principle of gauge invariance requires that the values of physically measurable quantities will be preserved upon changing the gauge in which electromagnetic quantities are expressed. It is emphasized here that physical interpretations do not depend only on laboratory measurables, but also upon other quantities that are altered by a gauge transformation. It is shown by a variety of simple examples that different gauges can lead to major changes in physical interpretations even though the electromagnetic fields are unaltered. The usual hypothesis that the radiation gauge (also known as the Coulomb gauge) is the “physical” gauge, in the sense that it meets the expectations of a laboratory interpretation, is supported by the various cases considered.

Green's function method in quantum chemistry: New numerical algorithm for the Dirac equation with complex energy and Fermi‐model nuclear potential

AbstractWe present a new effective approach to construction of the electron Green function for the Dirac equation with a nonsingular central nuclear Fermi‐model potential and complex energy. We represent the radial Green function as a combination of two fundamental solutions of the Dirac equation. The approach proposed includes a procedure of generating the relativistic electron functions Ψ with performance of the gauge invariance principle. To reach the gauge invariance principle performance, we use earlier developed QED perturbation theory approach. In the fourth order of the QED perturbation theory (PT) there are diagrams, whose contribution into imaginary part of radiation width ImdE for the multielectron system accounts for many‐body correlation effects. A minimization of the functional ImdE leads to integral‐differential Kohn‐Sham‐like density functional equations. Further check for the gauge principle performance is realized by means of the Ward identities. In the numerical procedure we use the effective algorithm, within which a definition of the Dirac equation fundamental solutions is reduced to solving the single system of the differential equations. This system includes also the differential equations for the Fermi‐model nuclear potential and equations for calculating the integrals of the ∫ ∫ dr1dr2 type in the Mohr formula for definition of the self‐energy shift to atomic levels energies. Such an approach allows to compensate a main source of the errors, connected with numerical integration ∫dξ and summation on χ in the Mohr expressions during calculating the self‐energy radiative correction to the atomic levels energies. Some numerical illustrations of applying the approach within QED PT to calculate the intermediate and high‐Z Li‐like ions transitions energies are presented. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

A Weyl-Cartan space-time model based on the gauge principle

Based on the requirement that the gauge invariance principle for the Poincare-Weyl group be satisfied for the space-time manifold, we construct a model of space-time with the geometric structure of a Weyl-Cartan space. We show that three types of fields must then be introduced as the gauge (“compensating”) fields: Lorentz, translational, and dilatational. Tetrad coefficients then become functions of these gauge fields. We propose a geometric interpretation of the Dirac scalar field. We obtain general equations for the gauge fields, whose sources can be the energy-momentum tensor, the total momentum, and the total dilatation current of an external field. We consider the example of a direct coupling of the gauge field to the orbital momentum of the spinor field. We propose a gravitational field Lagrangian with gauge-invariant transformations of the Poincare-Weyl group.

Gauge invariance in fractional field theories

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order o ( g ¯ ) in the coupling constant g ¯ . Based on the Riemann–Liouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non-relativistic fractional Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.

DECOMPOSITION OF SU(2) CONNECTION AND KNOT STRUCTURE IN SKYRME–FADDEEV MODEL

In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simple proposal. We also obtain the action of Skyrme–Faddeev model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. Then, the knot structure in Skyrme–Faddeev model is discussed in terms of the so-called ϕ-mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of ϕ-mapping, naturally. At last, we briefly discussed the topological invariant–Hopf invariant which describes the topology of these knots. It is shown that Hopf invariant is the total number of all the linking numbers and self-linking numbers of these knots.

Why the Standard Model

The Standard Model is based on the gauge invariance principle with gauge group U ( 1 ) × SU ( 2 ) × SU ( 3 ) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational explanation: space-time has a fine structure given as a product of a four-dimensional continuum by a finite noncommutative geometry F . The raison d’être for F is to correct the K -theoretic dimension from four to ten (modulo eight). We classify the irreducible finite noncommutative geometries of K -theoretic dimension six and show that the dimension (per generation) is a square of an integer k . Under an additional hypothesis of quaternion linearity, the geometry which reproduces the Standard Model is singled out (and one gets k = 4 ) with the correct quantum numbers for all fields. The spectral action applied to the product M × F delivers the full Standard Model, with neutrino mixing, coupled to gravity, and makes predictions (the number of generations is still an input).

Transgression forms and extensions of Chern-Simons gauge theories

A gauge invariant action principle, based on the idea of transgression forms, is proposed. The action extends the Chern-Simons form by the addition of a boundary term that makes the action gauge invariant (and not just quasi-invariant). Interpreting the spacetime manifold as cobordant to another one, the duplication of gauge fields in spacetime is avoided. The advantages of this approach are particularly noticeable for the gravitation theory described by a Chern-Simons lagrangian for the AdS group, in which case the action is regularized and finite for black hole geometries in diverse situations. Black hole thermodynamics is correctly reproduced using either a background field approach or a background-independent setting, even in cases with asymptotically nontrivial topologies. It is shown that the energy found from the thermodynamic analysis agrees with the surface integral obtained by direct application of Noether's theorem.

Quantum metastability in time-periodic potentials

In this paper, we investigate quantum metastability of a particle trapped in between an infinite wall and a square barrier, with either a time-periodically oscillating barrier (Model A) or bottom of the well (Model B). Based on the Floquet theory, we derive in each case an equation which determines the stability of the metastable system. We study the influence on the stability of two Floquet states when their Floquet energies (real part) encounter a direct or an avoided crossing at resonance. The effect of the amplitude of oscillation on the nature of crossing of Floquet energies is also discussed. It is found that by adiabatically changing the frequency and amplitude of the oscillation field, one can manipulate the stability of states in the well. By means of a discrete transform, the two models are shown to have exactly the same Floquet energy spectrum at the same oscillating amplitude and frequency. The equivalence of the models is also demonstrated by means of the principle of gauge invariance.

Local scale invariance, Cantorian space–time and unified field theory

Abstract We develop field theoretic arguments for the unification of relativistic gravity with standard model interactions on El Naschie's Cantorian space–time. The work proceeds by showing the equivalence between the fundamental principle of local gauge invariance and the local scale invariance of space–time and matter fields undergoing critical behavior on high-energy scales. We focus on the transition boundary between the classical and non-classical regimes, the latter being characterized by generalized scaling laws with continuously varying exponents. Both relativistic gravity and standard model interactions emerge from the underlying geometry of Cantorian space–time near this transition boundary.

Field-theory approach to the disintegration of bound systems on the basis of a local gauge nature of an electromagnetic field

An approach is developed that makes it possible to take into account the structure of bound (nonlocal) matter fields in photodisintegration processes with allowance for the requirements of the fundamental principles of covariance and gauge invariance. The approach is based on employing the local U(1) gauge nature of an electromagnetic field, whose vector potential is identified with a connection that performs a parallel transportation of matter-field operators in a fiber space with an interior charge symmetry along “minimum” trajectories.

Gauge Model with Massive Gravitons

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model has strict local gravitational gauge symmetry, and gauge theory of gravity is a perturbatively renormalizable quantum model. However, in the original model, all gauge gravitons are massless. We want to ask whether there exist massive gravitons in Nature. In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gauge field is introduced into the theory without violating the strict local gravitational gauge symmetry. Massive gravitons can be considered to be possible origin of dark energy and dark matter in the Universe.

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum, it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.