Principle Of Gauge Invariance Research Articles

On the effect of derivative interactions in quantum field theory

There exist several good reasons why one may wish to add a total derivative to an interaction in quantum field theory, e.g., in order to improve the perturbative construction. Unlike in classical field theory, adding derivatives in general changes the theory. The analysis whether and how this can be prevented is presently limited to perturbative orders gn, n≤3. We drastically simplify it by an all-orders formula, which also allows to answer some salient structural questions. The method is part of a larger program to (re)derive interactions of particles by quantum consistency conditions, rather than a classical principle of gauge invariance.

Study of characteristics elementary atomic processes in the neon-like multicharged ions plasma within an energy approach

We present the theoretical foundations of an advanced relativistic approach to computing the main energy, spectral characteristics of radiative-collisional processes in the plasma (in particular, the Debye plasma) of atomic as the example, neon-like) ions with simultaneous, quantitatively consistent consideration of the complex relativistic, interelectron exchange-correlation and plasma environment effects. The approach is based on the combination of a relativistic energy approach (S-matrix Gell-Mann and Low formalism), the relativistic gauge-invariant many-body perturbation theory with optimized Dirac-Fock-Sturm and Debye-Hückel approximations with accounting for the plasma environment effects with possible generalization on the presence of an additional external electromagnetic field. The fundamental point of our approach is the selection of the optimized Dirac-Fock-Sturm zeroth approximation and application of the consistent procedure for constructing a one-quasiparticle representation (basis’s of relativistic wave functions) in compliance with the principle of gauge invariance, in particular, by minimizing a gauge-noninvariant contributions to the radiative widths of the atomic (ionic) levels due to the complex exchange-correlation effects. The electron-ion collision strength and the dioelect5ron capture rate etc are determined within the presented theory.

Motley String Theory Overview

Copenhagen Update of Motley String Theory (aka MST) Overview includes several new results author obtained during his first two years in Denmark. Paper provides Overview of the basic principles of MST and demonstrates how it solved major problems of High Energy Physics and Astrophysics. New version also describes what "elementary particles" are made of from the MST point of view and provides details of the process of their creation. We mention that MST based analysis suggests that neutrinos are Majorana fermions and therefore neutrinoless double beta decay is to be detected sooner or later. After that we provide evidence for the rotational symmetry of MST being the fundamental reason for the principle of Gauge Invariance, which plays key role in the "classical" Particle Physics the Standard Model is based upon as well as in the Quantum Field Theory

ADVANCED STUDY OF SPECTRAL AND HYPERFINE STRUCTURE PARAMETERS FOR Li-LIKE MULTICHARGED IONS WITHIN Relativistic Theory

The relativistic many-body perturbation theory with the optimized Dirac zeroth approximation is applied to calculation of some fundamental characteristics of the hyperfine structure of middle and heavy Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with performance of the gauge invariance principle. There are listed the calculated values of derivatives of the one-electron characteristics, including the hyperfine structure parameters, on nuclear radius for the Li-like multicharged ions with the corresponding analysis.

THEORETICAL STUDY OF Rydberg ALKALI ATOMIC SYSTEMS in a Black-body radiation field: Relativistic APPROACH

We present the results of studying the characteristics of Rydberg alkali atomic systems in a black-body (BBR; thermal) radiation field, in particular, BBR induced Stark shift coefficient k. As theoretical approach the combined generalized relativistic energy approach and relativistic many-body perturbation theory (PT) with ab initio Dirac zeroth approximation is applied. Application of theory to computing the spectral parameters of studied atomic systems have demonstrated physically reasonable agreement between the theoretical and experimental data. carefully. It should be noted that our method takes carefully into account such important factors as the implementation of a gauge invariance principle when calculating the corresponding matrix elements, the correct degree of consideration of complex exchange-correlation effects (primarily, the effect of polarization of the core), and also generates a fairly optimal one-quasiparticle representation in within the limits of many-body relativistic PT with ab initio zeroth Dirac-Fock (Kohn-Sham) approximation. In any case, the formalism developed in this work, as it follows from the given results, can be used for precise calculations of the Stark shift coefficient k, the BBR shift parameter β, and other parameters.

RELATIVISTIC CALCULATION OF WAVELENGTHS AND E1 OSCILLATOR STRENGTHS IN Li-LIKE MULTICHARGED IONS AND GAUGE INVARIANCE PRINCIPLE

The spectral wavelengths and oscillator strengths for 1s22s (2S1/2) → 1s23p (2P1/2) transitions in the Li-like multicharged ions with the nuclear charge Z=28,30 are calculated on the basis of the combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order optimized Dirac-Kohn-Sham one-particle approximation and gauge invariance principle performance. The comparison of the obtained results with available theoretical and experimental (compilated) data is performed. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth order that significantly provides a physically reasonable agreement between theory and precise experiment.

Heat transport in liquid water from first-principles and deep neural network simulations

We compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represented by a deep neural network (DNN) trained on DFT data, whereby the PES has an explicit local decomposition and the energy flux takes a particularly simple expression. By virtue of a gauge invariance principle, established by Marcolongo, Umari, and Baroni, the two approaches should be equivalent if the PES were reproduced accurately by the DNN model. We test this hypothesis by calculating the thermal conductivity, at the GGA (PBE) level of theory, using the direct formulation and its DNN proxy, finding that both approaches yield the same conductivity, in excess of the experimental value by approximately 60%. Besides being numerically much more efficient than its direct DFT counterpart, the DNN scheme has the advantage of being easily applicable to more sophisticated DFT approximations, such as meta-GGA and hybrid functionals, for which it would be hard to derive analytically the expression of the energy flux. We find in this way, that a DNN model, trained on meta-GGA (SCAN) data, reduce the deviation from experiment of the predicted thermal conductivity by about 50%, leaving the question open as to whether the residual error is due to deficiencies of the functional, to a neglect of nuclear quantum effects in the atomic dynamics, or, likely, to a combination of the two.

The foundation of the hyperunified field theory II — Fundamental interaction and evolving universe

In part I of the foundation of the hyperunified field theory, we have shown the presence of entangled hyperqubit-spinor field as fundamental building block with appearance of Minkowski hyper-space–time as free-motion space–time and emergence of inhomogeneous hyperspin symmetry as fundamental symmetry. In this paper as part II, we demonstrate by following along gauge invariance principle and scaling invariance hypothesis that the inhomogeneous hyperspin gauge symmetry and scaling gauge symmetry govern fundamental interactions and reveal the nature of gravity and space–time. With the fiber bundle structure of biframe hyper-space–time and emergence of noncommutative geometry, we explore methodically the gauge-geometry duality and genesis of gravitational interaction in locally flat gravigauge hyper-space–time. A whole hyperunified field theory in 19-dimensional hyper-space–time is established to unify not only all discovered leptons and quarks into hyperunified qubit-spinor field but also all known basic forces into hyperunified interaction governed by inhomogeneous hyperspin gauge symmetry. We present a systematic investigation on the hyperunified field theory by deriving the dynamics of fundamental fields as basic laws of nature and conservation laws relative to basic symmetries and showing Higgs-like bosons and three families of lepton–quark states. We provide a detailed analysis on inflationary early universe with evolving graviscalar field and a discussion on scaling gauge field as dark matter candidate and [Formula: see text]-spin scalar field as source of dark energy.

Gauge-field-induced torsion and cosmic inflation

In this paper, inflation in the framework of Einstein–Cartan theory is revisited. Einstein–Cartan theory is a natural extension of the General Relativity with nonvanishing torsion. The connection on Riemann–Cartan space–time is only compatible with the cosmological principal for a particular form of torsion. We also show this form to be compatible with gauge invariance principle for non-Abelian and Abelian gauge fields under a certain deviced coupling procedure. We adopt an Abelian gauge field in the form of “cosmic triad”. The dynamical field equations are obtained and shown to sustain cosmic inflation with a large number of e-folds. We emphasize that at the end of inflation, torsion vanishes and the theory of Einstein–Cartan reduces to the General Relativity with the usual FRW geometry.

Generalized Holographic Principle, Gauge Invariance and the Emergence of Gravity à la Wilczek

We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle entails a general principle of gauge invariance. When this is realized in an ambient Lorentzian space-time, gauge invariance under the Poincaré group is immediately achieved. We apply this pathway to retrieve the action of gravity. The latter is cast à la Wilczek through a similar formulation derived by MacDowell and Mansouri, which involves the representation theory of the Lie groups SO(3,2) and SO(4,1).

Superconducting properties of bi-layer graphene in chiral model

Within the scope of the graphene chiral model we suggest a description of superconducting properties of the bi-layer graphene with some twisting angle a between the layers. The interaction with an external magnetic field is included through the gauge invariance principle, the field being oriented along the graphene plane. The expression for the optimal twisting angle generating superconductivity is obtained, the latter being equivalent to the vanishing magnetic field between the graphene layers (the Meissner effect).

HYPERFINE STRUCTURE PARAMETERS FOR Li-LIKE MULTICHARGED IONS WITHIN RELATIVISTIC MANY-BODY PERTURBATION THEORY

The relativistic many-body perturbation theory with the optimized Dirac-Kohn-Sham zeroth approximation is applied to calculation of the hyperfine structure parameters for some Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with fulfilment of the gauge invariance principle. The obtained data on the hyperfine structure parameters of the Li-like multicharged ions are analyzed and compared with alternative theoretical and experimental results.

Physics architecture. Part two

Physics architecture. Part two. The talk is devoted to the jubilee of academician M.A. Markov, who was born in 1908. Now we have also the 100th anniversary of the gauge invariance principle proposed by Weyl in 1918. During the period from 1967 to 1988 M.A. Markov was Academician Secretary of Nuclear Physics Department of AN USSR. He organized the series of conferences dedicated to the topical problems of theoretical, nuclear and elementary particle physics. One of them was international seminar “Vector mesons and electromagnetic interactions” under A.M. Baldin direct leadership. It went off in JINR in September of 1969. This very that seminar gave birth to the conferences series named “Baldin autumn”. Thanks to the discussions at the A.M. Baldin seminar many critical situations in theoretical and experimental physics were subsequently settled. The first plenary session of the seminar included L.D. Faddeev talk about gauge field quantization, which cleared the way to develop the renormalized quantum gauge field theory. My talk was dedicated to the transformation of the classical gauge field theory into geometrical one. As a result the unified geometrical theory was obtained, which could include any interactions together with Einsteinian gravity. In this connection both formulations of Weyl’s local gauge invariance principle (of 1918 and 1929) as well as Einsteinian principle of general relativity were used. This approach was based on the fibre bundle geometry, which was developed by mathematicians at that time. This theory gives a realizable classification of interactions according to the local Lie’s symmetry groups associated with them. This approach leads to the VIth Hilbert’s problem solution. To obtain further development of the gauge field theory, it is necessary to decide the question of the gauge field mass origin. It is the key moment both in quantum and geometrical classical theories of the gauge fields. Therefore it is very important to analyze the experiments, where massive and massless particles are converted in each other (similar Baldin experiments in JINR in 1967).

Хвильові і осциляторні сильні сторони Li-подібних багатозарядних іонів в рамках теорії відносного збудження багатьох тіл

The relativistic many-body perturbation theory with the optimized Dirac-Kohn-Sham zeroth approximation is applied to calculation of the radiative transitions wavelengths and oscillator strengths for some Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with fulfilment of the gauge invariance principle. An accurate treatment of the QED perturbation theory fourth order (a second order of the atomic perturbation theory) Feynman diagrams (whose contribution into the energy shift imaginary part (radiation width) for the multi-electron atoms accounts for multi-body correlation effects) is performed. The obtained data on the radiative transition wavelengths and oscillator strengths for some transition in spectra of the Li-like multicharged ions are analyzed and compared with alternative theoretical and experimental results.

Expansion of Einstein-Yang-Mills amplitude

In this paper, we study from various perspectives the expansion of tree level single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes. By applying the gauge invariance principle, a programable recursive construction is devised to expand EYM amplitude with arbitrary number of gravitons into EYM amplitudes with fewer gravitons. Based on this recursive technique we write down the complete expansion of any single trace EYM amplitude in the basis of color-order Yang-Mills amplitude. As a byproduct, an algorithm for constructing a polynomial form of the BCJ numerator for Yang-Mills amplitudes is also outlined in this paper. In addition, by applying BCFW recursion relation we show how to arrive at the same EYM amplitude expansion from the on-shell perspective. And we examine the EYM expansion using KLT relations and show how to evaluate the expansion coefficients efficiently.

Gauge theory of massless spin- field in de Sitter space-time

On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known fundamental interactions of elementary particles, from electromagnetism and weak interactions to strong interactions and gravity. This paper presents a procedure for defining the gauge-covariant derivative and gauge invariant Lagrangian density in de Sitter ambient space-time formalism. The gauge invariant field equation is then explicitly calculated in detail for a massless spin- gauge field.

On the two remaning issues in the gauge-invariant decomposition problem of the nucleon spin

The question whether the total angular momentum of the gluon in the nucleon can be decomposed into its spin and orbital parts without conflict with the gauge-invariance principle has been an object of long-lasting debate. Despite a remarkable progress achieved through the recent intensive researches, the following two issues still remains to be clarified more transparently. The first issue is to resolve the apparent conflict between the proposed gauge-invariant decomposition of the total gluon angular momentum and the textbook statement that the total angular momentum of the photon cannot be gauge-invariantly decomposed into its spin and orbital parts. We show that this problem is also intimately connected with the uniqueness or nonuniqueness problem of the nucleon spin decomposition. The second practically more important issue is: among the two physically inequivalent decompositions of the nucleon spin, i.e. the “canonical” type decomposition and the “mechanical” type decomposition, which can we say is more physical or closer to direct observation? In the present paper, we try to answer both these questions as clearly as possible.

Problems related to gauge invariance and momentum, spin decomposition in nucleon structure study

How do the quark and gluon share the nucleon momentum? How does the nucleon spin distribute among its constituents? What means the quark and gluon momentum, spin and orbital angular momentum? These problems are analyzed and a solution is proposed based on {\it gauge invariance principle, canonical quantization rule and Poincar$\acute{e}$ covariance}.

Towards gauge-independent treatment of radiative capture in nuclear reactions: Applications to low-energy cluster-cluster collisions

Our departure point in describing electromagnetic (EM) interactions with nuclei (in general, bound systems of charged particles) is to use the Fock-Weyl criterion and a generalization of the Siegert theorem. It is shown how one can meet the gauge invariance principle (GIP) in all orders in the charge and construct the corresponding EM interaction operators in case of nuclear forces arbitrarily dependent on velocity. Along the guideline we have derived the conserved current density operator for a dicluster system (more precisely, the system of two finite-size clusters with many-body interaction effects included). In the context, we are addressing the current clusterization as a first step when accounting for possible cluster excitations. Being expressed through the electric and magnetic field strengths and matrix elements of the so-called generalized electric and magnetic dipole moments of the system, associated with the conserved current, the single-photon transition amplitude attains a manifestly gauge-independent (GI) form. The latter is essentially simplified at low energies.

Gauge invariance, canonical quantization and Poincaré covariance in nucleon structure

There are different quark and gluon momentum, spin and orbital angular momentum operators used in the study of nucleon structure. We analyze the physical contents of these operators and propose a new set of operators based on gauge invariance principle, canonical quantization rule and Poincaré covariance. Atomic structure is a simpler testing ground of these operators and has been analyzed together. These new operators are the gauge invariant version of the gauge non-invariant canonical version used in physics since the establishment of quantum mechanics and reduce to the familiar canonical ones in Coulomb gauge.