Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge

We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space. The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime metric has a simple form in terms of the phase space variables. With gauge group SO (3, C), the theory equals the Ashtekar formulation of gravity with a cosmological constant. For Lorentzian signature, the theory is complex, and we have not found any good reality conditions. In the Euclidean signature case, everything is real. In a weak field expansion around de Sitter spacetime, the theory is shown to give the conventional Yang-Mills theory to the lowest order in the fields. We show that the coupling to a Higgs scalar is straightforward, while the naive spinor coupling does not work. We have not found any way of including spinors that gives a closed constraint algebra. For gauge group U(2), we find a static and spherically symmetric solution.

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The multipolar Hamiltonian in radiation theory

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1980.0112 ◽

1980 ◽

Vol 372 (1749) ◽

pp. 265-273 ◽

Cited By ~ 40

Keyword(s):

Quantum Optics ◽

Quantum Electrodynamics ◽

Electrostatic Interactions ◽

Scalar Potential ◽

Theoretical Chemistry ◽

Coulomb Gauge ◽

Radiation Theory ◽

Initial Choice ◽

Arbitrary Gauge

The multipolar Hamiltonian is widely used in applications of quantum electrodynamics to quantum optics and theoretical chemistry. In this paper, it is shown how this form of the Hamiltonian, normally derived within the Coulomb gauge, may be obtained from a Lagrangian in an arbitrary gauge. The method involves the construction of the Routhian functional to eliminate ignorable coordinates from which the Hamiltonian is obtained. Further, the electrostatic interactions arise from a constraint and are independent of the initial choice of the scalar potential. The contributions from Röntgen currents, arising from dielectric motion, are allowed for by including nuclear motions in the theory.

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Derivation of the Power-Zienau-Woolley Hamiltonian in quantum electrodynamics by gauge transformation

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1983.0022 ◽

1983 ◽

Vol 385 (1789) ◽

pp. 439-460 ◽

Cited By ~ 60

Keyword(s):

Gauge Transformation ◽

Quantum Electrodynamics ◽

Unitary Transformation ◽

Scalar Potential ◽

Coupled System ◽

Initial Vector ◽

Transformation Theory ◽

Gauge Transformations ◽

New Formulation ◽

Arbitrary Gauge

The different forms of Hamiltonian for the coupled system consisting of the electromagnetic field and a non-relativistic charged particle are considered in the context of gauge-transformation theory. The conventional Lagrangian of the system in an arbitrary gauge is converted to a new form by transformation to another arbitrary gauge, and a new formulation of the theory is obtained by expressing the new Lagrangian in terms of the initial potentials. Thus different gauge transformations produce different momenta ∏ conjugate to the initial vector potential A , and hence different forms of Hamiltonian. The transformations that produce the Coulomb-gauge and Power-Zienau-Woolley (P. Z. W.) Hamiltonians are considered in detail. It is shown that ∏ is transverse in both cases and only the transverse part of A is accordingly involved in the field quantization; neither the longitudinal part of A nor the scalar potential appears explicitly, the instantaneous Coulomb energies being included via an electronic polarization determined by the gauge generator. The transformations between gauges are illustrated by simple diagrammatic representations of A and ∏ . Compararison with the commonly used unitary transformation derivation of the P. Z. W. Hamiltonian emphasizes the need for a careful reinterpretation of the physical significance of ∏ after the unitary transformation has been made.

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The internal conversion of gamma-rays.—Part II

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1928.0208 ◽

1928 ◽

Vol 121 (787) ◽

pp. 447-456

Keyword(s):

Magnetic Field ◽

Quantum Mechanics ◽

Wave Equation ◽

Gamma Rays ◽

Internal Conversion ◽

Scalar Potential ◽

X Ray ◽

Electro Magnetic Field ◽

Γ Rays ◽

Electro Magnetic

In a previous paper the absorption of γ-rays in the K-X-ray levels of the atom in which they are emitted was calculated according to the Quantum Mechanics, supposing the γ-rays to be emitted from a doublet of moment f ( t ) at the centre of the atom. The non-relativity wave equation derived from the relativity wave equation for an electron of charge — ε moving in an electro-magnetic field of vector potential K and scalar potential V is h 2 ∇ 2 ϕ + 2μ ( ih ∂/∂ t + εV + ih ε/μ c (K. grad)) ϕ = 0. (1) Suppose, however, that K involves the space co-ordinates. Then, (K. grad) ϕ ≠ (grad . K) ϕ , and the expression (K . grad) ϕ is not Hermitic. Equation (1) cannot therefore be the correct non-relativity wave equation for a single electron in an electron agnetic field, and we must substitute h 2 ∇ 2 ϕ + 2μ ( ih ∂/∂ t + εV) ϕ + ih ε/ c ((K. grad) ϕ + (grad. K) ϕ ) = 0. (2)

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Systematics of type IIA moduli stabilisation

Journal of High Energy Physics ◽

10.1007/jhep11(2020)113 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Fernando Marchesano ◽

David Prieto ◽

Joan Quirant ◽

Pramod Shukla

Keyword(s):

Scalar Potential ◽

Systematic Search ◽

Stability Criteria ◽

De Sitter ◽

Large Subset

Abstract We analyse the flux-induced scalar potential for type IIA orientifolds in the presence of p-form, geometric and non-geometric fluxes. Just like in the Calabi-Yau case, the potential presents a bilinear structure, with a factorised dependence on axions and saxions. This feature allows one to perform a systematic search for vacua, which we implement for the case of geometric backgrounds. Guided by stability criteria, we consider configurations with a particular on-shell F-term pattern, and show that no de Sitter extrema are allowed for them. We classify branches of supersymmetric and non-supersymmetric vacua, and argue that the latter are perturbatively stable for a large subset of them. Our solutions reproduce and generalise previous results in the literature, obtained either from the 4d or 10d viewpoint.

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Linear Energy Density and the Flux of an Electric Field in Proca Tubes

Symmetry ◽

10.3390/sym13040640 ◽

2021 ◽

Vol 13 (4) ◽

pp. 640

Author(s):

Vladimir Dzhunushaliev ◽

Vladimir Folomeev ◽

Abylaikhan Tlemisov

Keyword(s):

Scalar Field ◽

Electric Field ◽

Higgs Field ◽

Meissner Effect ◽

Coupling Constant ◽

Cylindrically Symmetric ◽

Integral Characteristics ◽

Energy And Momentum ◽

Energy And Momentum Densities ◽

Higgs Scalar

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the existence of such tubes depends crucially on the presence of the Higgs field (there are no such solutions without this field). We examine the dependence of the integral characteristics (linear energy and momentum densities) on the values of the electromagnetic potentials at the center of the tube, as well as on the values of the coupling constant of the Higgs scalar field. The solutions obtained are topologically trivial and demonstrate the dual Meissner effect: the electric field is pushed out by the Higgs scalar field.

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Harmonic hybrid inflation

Journal of High Energy Physics ◽

10.1007/jhep12(2020)161 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Federico Carta ◽

Nicole Righi ◽

Yvette Welling ◽

Alexander Westphal

Keyword(s):

Domain Wall ◽

Symmetry Breaking ◽

Initial Conditions ◽

Scalar Potential ◽

Field Range ◽

Slow Roll ◽

Minimal Form ◽

Wide Range ◽

Hybrid Inflation ◽

Type Iib String Theory

Abstract We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of the scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints f ≲ MP and ∆ϕ60 ≲ MP on the axion periodicity and slow-roll field range, respectively. We discuss controlled ℤ2-symmetry breaking of the adjacent axion vacua as a means of avoiding cosmological domain wall problems. Including a minimal form of ℤ2-symmetry breaking into the minimally tuned setup leads to a prediction of primordial tensor modes with the tensor-to-scalar ratio in the range 10−4 ≲ r ≲ 0.01, directly accessible to upcoming CMB observations. Finally, we outline several avenues towards realizing harmonic hybrid inflation in type IIB string theory.

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Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark

Journal of High Energy Physics ◽

10.1007/jhep01(2021)180 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Guillem Domènech ◽

Mark Goodsell ◽

Christof Wetterich

Keyword(s):

Quantum Gravity ◽

Top Quark ◽

Quark Mass ◽

Scalar Potential ◽

Planck Scale ◽

Neutrino Masses ◽

Top Quark Mass ◽

Vacuum Stability ◽

Intermediate Scale ◽

Yukawa Couplings

Abstract A general prediction from asymptotically safe quantum gravity is the approximate vanishing of all quartic scalar couplings at the UV fixed point beyond the Planck scale. A vanishing Higgs doublet quartic coupling near the Planck scale translates into a prediction for the ratio between the mass of the Higgs boson MH and the top quark Mt. If only the standard model particles contribute to the running of couplings below the Planck mass, the observed MH∼ 125 GeV results in the prediction for the top quark mass Mt∼ 171 GeV, in agreement with recent measurements. In this work, we study how the asymptotic safety prediction for the top quark mass is affected by possible physics at an intermediate scale. We investigate the effect of an SU(2) triplet scalar and right-handed neutrinos, needed to explain the tiny mass of left-handed neutrinos. For pure seesaw II, with no or very heavy right handed neutrinos, the top mass can increase to Mt ∼ 172.5 GeV for a triplet mass of M∆ ∼ 108GeV. Right handed neutrino masses at an intermediate scale increase the uncertainty of the predictions of Mt due to unknown Yukawa couplings of the right-handed neutrinos and a cubic interaction in the scalar potential. For an appropriate range of Yukawa couplings there is no longer an issue of vacuum stability.

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Effective Scalar Potential in Asymptotically Safe Quantum Gravity

Universe ◽

10.3390/universe7020045 ◽

2021 ◽

Vol 7 (2) ◽

pp. 45

Author(s):

Christof Wetterich

Keyword(s):

Quantum Gravity ◽

Top Quark ◽

Particle Physics ◽

Scalar Potential ◽

Scalar Fields ◽

The Standard Model ◽

Scaling Potential ◽

Realistic Description ◽

The Masses ◽

Dynamical Dark Energy

We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy.

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