Equivalence Between the Fock-Schwinger Gauge and the Feynman Gauge

Delbourgo, R.; Triyanta,

doi:10.1142/s0217751x92002659

Cited by 12 publications

(8 citation statements)

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“…Electromagnetic potentials of the same form as Bloch's [7] have been later proposed by other authors. [8][9][10][11] A simple compact expression, [12][13][14][15][16][17] defining a gauge customarily referred to as Poincar e's, ‡ [12,17] provides a power series for the vector potential equivalent to Bloch's. [18][19][20][21][22] The new potentials, Eqs.…”

Section: R5mentioning

confidence: 99%

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Invariance of molecular response properties under a coordinate translation

Lazzeretti

2014

Int J of Quantum Chemistry

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The response of a molecule to static and dynamic electromagnetic fields and intramolecular perturbations is reviewed within the framework of the Rayleigh-Schr€ odinger perturbation theory. A semiclassical approach is adopted, using quantized form of electronic operators and the nonquantized description of the electromagnetic fields via the Maxwell equations. The Bloch multipolar gauge has been used to define operators suitable to describe the molecular interaction with nonhomogneous timedependent perturbations. It is shown that the quantum mechanical theory of magnetic properties can profitably be proposed in terms of electronic current densities induced by an external magnetic field and permanent magnetic dipole moments at the nuclei. Theoretical relationships are reported to evaluate magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, proving that the whole theory can be reformulated via the equations of classical electromagnetism, provided that the current density is evaluated by quantum mechanical methods. Emphasis is placed on the invariance of response properties in a translation of the coordinate system as a basic requirement for measurability. The connections among translational invariance, gauge invariance, and electron charge conservation are outlined, showing that they can be illustrated via quantum mechanical sum rules. A number of relationships describing the change of static and dynamic electromagnetic properties in a translation of the reference frame are reported.

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Section: R5mentioning

confidence: 99%

“…[4,7,18] A number of different alternative denominations can be found in the literature, see note a, first page of Refs. [16] and [17].…”

Section: R5mentioning

confidence: 99%

Invariance of molecular response properties under a coordinate translation

Lazzeretti

2014

Int J of Quantum Chemistry

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“…34 The orbital anapole moment of a molecule is an intrina) E-mail: lazzeret@unimo.it sic electronic property which can be rationalized via anapole magnetizabilities, 29,[35][36][37][38][39][40][41][42] allowing for a magnetic multipole expansion based on the Bloch gauge [43][44][45] later rediscovered by others. [46][47][48][49] A simple compact expression, [50][51][52][53][54][55] defining a gauge usually referred to as Poincaré's, 50,55,56 yields a power series for the vector potential equivalent to Bloch's. [57][58][59][60] The present paper is aimed at computing translationally invariant diagonal components and average values of anapole magnetizability in cyclic compounds with chemical formula C 4 H 4 X 2 , with X=O, S, Se, and Te.…”

Section: Introductionmentioning

confidence: 99%

Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

Pagola

Ferraro

Provasi

et al. 2014

The Journal of Chemical Physics

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Calculations have been carried out for C4H4X2 cyclic molecules, with X=O, S, Se, and Te, characterized by the presence of magnetic-field induced toroidal electron currents and associated orbital anapole moments. The orbital anapole induced by a static nonuniform magnetic field B, with uniform curl C=∇×B, is rationalized via a second-rank anapole magnetizability tensor a(αβ), defined as minus the second derivative of the second-order interaction energy with respect to the components C(α) and B(β). The average anapole magnetizability a̅ equals -χ̅, the pseudoscalar obtained by spatial averaging of the dipole-quadrupole magnetizability χ(α,βγ). It has different sign for D and L enantiomeric systems and can therefore be used for chiral discrimination. Therefore, in an isotropic chiral medium, a homogeneous magnetic field induces an electronic anapole A(α), having the same magnitude, but opposite sign, for two enantiomorphs.

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“…For heavy quarks running in two-loop diagrams in Fig. 2, we calculate the amplitude using the Fock-Schwinger gauge [35][36][37][38] for the gluon background field in zero momentum limit [9,14,39,40]. The complete two-loop matrix elements with two Z running in the loop in the Fig.…”

Section: Coherent Elastic Neutrino-nucleus Scatteringmentioning

confidence: 99%

Loop effect with vector mediator in the coherent neutrino-nucleus scattering

Chao,

Li,

Liao

et al. 2021

Preprint

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The active neutrinos can convert into a new exotic fermion χ through coherent neutrino-nucleus scattering νN → χN and thus the ν − χ interaction leads to novel recoil spectrum in the neutrino scattering experiments. We study the general neutrino interactions by evaluating both the tree-level and loop-level contributions to the coherent elastic neutrino-nucleus scattering (CEνNS). The loop diagrams produce active neutrino elastic scattering process νN → νN with the fermion χ inside the loops. The neutrino interaction is illustrated by the framework of a simplified neutrino model in which a new Dirac fermion χ interacts with active neutrinos and a leptophobic vector mediator Z . For the Z q q coupling being vector type and axialvector type, the CEνNS processes are dominated by the tree-level and loop-level contribution, respectively.We investigate the constraints on the couplings between Z and the new particle χ or the Standard Model quarks by fitting to the COHERENT data. The parameter space with m χ larger than the maximal energy of incoming neutrinos can also be constrained by including the loop-level contribution. More importantly, the inclusion of loop diagrams can place constraint on axial-vector interaction whose the tree-level process is absent in the coherent neutrino-nucleus scattering.

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Equivalence Between the Fock-Schwinger Gauge and the Feynman Gauge

Cited by 12 publications

References 0 publications

Invariance of molecular response properties under a coordinate translation

Invariance of molecular response properties under a coordinate translation

Theoretical estimates of the anapole magnetizabilities of C4H4X2 cyclic molecules for X=O, S, Se, and Te

Loop effect with vector mediator in the coherent neutrino-nucleus scattering

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