Search results for "formula"
showing 10 items of 755 documents
Symmetries in the Standard Model
2020
Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last decades in Particle Physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetry requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact Colour SU(3) local gauge symmetry. Parity violation in weak interactions led to consider the chi…
Massive Spin One and Renormalizable Gauges
2015
For many decades of the last century, physicists were struggling to define consistent (renormalizable and unitarity preserving) models for spin-one massive particles (Proca fields). As we know, this was beautifully achieved by Weinberg, Salam and Glashow in 1967 when they proposed an electroweak unified theory which we now call the Standard Model. The electroweak symmetry breaking mechanism, among other things, generates mass terms for the W and Z bosons, while preserving renormalizability and unitarity. The longitudinal degrees of freedom of the massive spin-one particles are given by the Goldostone bosons. Choosing one gauge or another might seem just a matter of convenience and in most c…
New Information on Nuclear Structure in the Cd-In-Sn Region from Laser Spectroscopy and the Question of Core Polarization Contribution to Nuclear Rad…
1986
Nuclear spin, moments and isotope shifts of charge radii have been measured by laser spectroscopy for about 70 nuclear states in the range 48 ≦ Z ≦ 50, 54 ≦ N ≦ 78. 1/2--states in heavy In-isotopes cross the Schmidt line, indicating complex nuclear structure. Magnetic as well as spectroscopic quadrupole moments of most of the odd odd In-isotopes can be reproduced satisfactorily by coupling the respective experimental moments of odd even and even odd neighbouring nuclei. The isotope shift of all three elements exhibits a parabolic shape, which is superimposed to the almost linear droplet model expectation. The shape can be fitted quantitatively to Talmis core polarization model. The curvatur…
Quantum Spin-Tunneling:A Path Integral Approach
1995
We investigate the quantum tunneling of a large spin in a crystal field and an external magnetic field. The twofold degeneracy of the corresponding classical ground state is removed due to tunneling. The tunnel splitting ΔE o of the ground state is calculated by use of a path integral formalism. It is shown that coherent spin state path integrals do not yield a reasonable result. However a “bosonlzation” of the spin system yields excellent results in the semiclassical limit. This result follows from the coherent spin state approach from replacing the spin quantum number s by s + 1/2 which causes a renormalization of the preexponential factor of ΔE o .
Prediction for magnetic moment of the muon informs a test of the standard model of particle physics
2021
A new first-principles computation of the effect that creates most uncertainty in calculations of the magnetic moment of the muon particle has been reported. The results might resolve a long-standing puzzle, but pose another conundrum. Fresh evidence in a longstanding puzzle of particle physics.
Lepton Flavour Violation in SUSY SO(10)
2008
The study of rare processes, which are suppressed or even forbidden in the Standard Model (SM) of particle physics, has been considered for a long time a powerful tool in order to shed light on new physics, especially for testing low-energy supersymmetry (SUSY). Indeed, taking into account the fact that neutrinos have mass and mix, the Standard Model predicts Lepton Flavour Violating (LFV) processes in the charged sector to occur at a negligible rate [1]. As a consequence, the discovery of such processes would be an unambigous signal of physics beyond the Standard Model. In the present years, we are experiencing a great experimental effort in searching for LFV processes; several experiments…
Towards the field theory of the Standard Model on fractional D6-branes on T6 /ℤ6 ′ : Yukawa couplings and masses
2012
We present the perturbative Yukawa couplings of the Standard Model on fractional intersecting D6-branes on T6/Z6' and discuss two mechanisms of creating mass terms for the vector-like particles in the matter spectrum, through perturbative three-point couplings and through continuous D6-brane displacements.
Note on the super-extended Moyal formalism and its BBGKY hierarchy
2017
We consider the path integral associated to the Moyal formalism for quantum mechanics extended to contain higher differential forms by means of Grassmann odd fields. After revisiting some properties of the functional integral associated to the (super-extended) Moyal formalism, we give a convenient functional derivation of the BBGKY hierarchy in this framework. In this case the distribution functions depend also on the Grassmann odd fields.
Classical Geometric Phases: Foucault and Euler
2020
In the last chapter we saw how a quantum system can give rise to a Berry phase, by studying the adiabatic round trip of its quantum state on a certain parameter space. Rather than considering what happens to states in Hilbert space, we now turn to classical mechanics, where we are concerned instead with the evolution of the system in configuration space. As a first example, we are interested in the geometric phase of an oscillator that is constrained to a plane that is transported over some surface which moves along a certain path in three-dimensional space. Contrary to determining the Berry phase, there is no adiabatic approximation of the motion along the curve involved. The Foucault phas…
Differential Geometry of Curves and Surfaces
2001
The goal of this article is to present the relation between some differential formulas, like the Gauss integral for a link, or the integral of the Gaussian curvature on a surface, and topological invariants like the linking number or the Euler characteristic.