Search results for "Formulation"

Muon (g− 2) in the Standard Model and supersymmetric extensions

2016

Recent new results on the SM and the SUSY prediction for the muon ( g – 2) are briefly reviewed, and a SUSY scenario with particularly large contributions is discussed.

QED one-loop corrections to radiative muon decay

1994

Based upon the Fermi interaction, the differential decay rate of the radiative muon decay including one-loop radiative corrections is determined to the order ${G}_{F}^{2}{\ensuremath{\alpha}}^{2}$. Essential aspects of the calculation are exhibited. After cancellation of IR divergences, the double radiative muon decay is included. Some initial applications are considered.

Lattice QCD: A Brief Introduction

2014

A general introduction to lattice QCD is given. The reader is assumed to have some basic familiarity with the path integral representation of quantum field theory. Emphasis is placed on showing that the lattice regularization provides a robust conceptual and computational framework within quantum field theory. The goal is to provide a useful overview, with many references pointing to the following chapters and to freely available lecture series for more in-depth treatments of specifics topics.

Examples for Calculating Path Integrals

2001

We now want to compute the kernel K(b, a) for a few simple Lagrangians. We have already found for the one-dimensional case that $$\displaystyle{ K{\bigl (x_{2},t_{2};x_{1},t_{1}\bigr )} =\int _{ x(t_{1})=x_{1}}^{x(t_{2})=x_{2} }[dx(t)]\,\text{e}^{(\mathrm{i}/\hslash )S} }$$ (19.1) with $$\displaystyle{ S =\int _{ t_{1}}^{t_{2} }dt\,L(x,\dot{x};t)\;. }$$ First we consider a free particle, $$\displaystyle{ L = m\dot{x}^{2}/2\;, }$$ (19.2) and represent an arbitrary path in the form, $$\displaystyle{ x(t) =\bar{ x}(t) + y(t)\;. }$$ (19.3) Here, \(\bar{x}(t)\) is the actual classical path, i.e., solution to the Euler–Lagrange equation: $$\displaystyle{ \frac{\partial L} {\partial x}\Big\vert _{…

Mean field methods in large amplitude nuclear collective motion

1984

The time dependent Hartree-Fock method (TDHF) is reviewed and its success and failure are discussed. It is demonstrated that TDHF is a semiclassical theory which is basically able to describe the time evolution of one-body operators, the energy loss in inclusive deep inelastic collisions, and fusion reactions above the Coulomb barrier. For genuine quantum mechanical processes as e.g. spontaneous fission, subbarrier fusion, phase shifts and the description of bound vibrations, the quantized adiabatic time dependent Hartree-Fock theory (quantized ATDHF) is suggested and reviewed. Realistic three-dimensional calculations for heavy ion systems of A1+A2<32 are presented. Applications to various …

Erratum to: Classical and Quantum Dynamics: From Classical Paths to Path Integrals

2017

Propagators for Particles in an External Magnetic Field

2001

In order to describe the propagation of a scalar particle in an external potential, we begin again with the path integral $$ K(r',t';r,0) = \int_{r,(0)}^{r',(t')} {[dr(t)]} \exp \left\{ {\frac{{\text{i}}} {\hbar }S[r(t)]} \right\} $$ (1) with $$ S[r(t)] = \int_0^{t'} {dt} L(r,\dot r). $$

Effective Lagrangian approach to neutrinoless double beta decay and neutrino masses

2012

Neutrinoless double beta ($0\nu\beta\beta$) decay can in general produce electrons of either chirality, in contrast with the minimal Standard Model (SM) extension with only the addition of the Weinberg operator, which predicts two left-handed electrons in the final state. We classify the lepton number violating (LNV) effective operators with two leptons of either chirality but no quarks, ordered according to the magnitude of their contribution to \znbb decay. We point out that, for each of the three chirality assignments, $e_Le_L, e_Le_R$ and $e_Re_R$, there is only one LNV operator of the corresponding type to lowest order, and these have dimensions 5, 7 and 9, respectively. Neutrino masse…

The CP-Conserving Direction

1998

A symmetry transformation is well defined in the case of an invariant theory, being the corresponding operator undetermined otherwise. However, we show that, even with CP violation, it is possible to determine the CP transformation by separating the Lagrangian of the Standard Model in a CP-conserving and a CP-violating part, in a unique way, making use of the empirically known quark mixing hierarchy. To order \lambda^3 for the Bd-system, the CP-conserving direction matches one of the sides of the (bd) unitarity triangle. We use this determination to calculate the rephasing invariant parameter \epsilon, which measures CP-mixing in the B0-B0bar system.

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…