arXiv subjects

N. L. Harshman

Publications and source records attributed to N. L. Harshman.

41 records · Page 3Linked to original sources

arXiv2003

Visualizing the Mass and Width Spectrum of Unstable Particles

Several graphical representations of the mass and width spectrum of unstable subatomic particles are presented. Such plots are useful tools for introducing students to the particle zoo and provide students an alternate way to organize conceptually what can seem like an overwhelming amount of data. In particular, such graphs highlight phenomenological features of unstable particles characteristic of different energy and time scales.

physics.ed-ph↗

arXiv2002

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.

quant-ph↗

arXiv2000

On the Mass and Width of the Z-boson and Other Relativistic Quasistable Particles

The ambiguity in the definition for the mass and width of relativistic resonances is discussed, in particular for the case of the Z-boson. This ambiguity can be removed by requiring that a resonance's width $Γ$ (defined by a Breit-Wigner lineshape) and lifetime $τ$ (defined by the exponential law) always and exactly fulfill the relation $Γ= \hbar/τ$. To justify this one needs relativistic Gamow vectors which in turn define the resonance's mass M_R as the real part of the square root $\rm{Re}\sqrt{s_R}$ of the S-matrix pole position s_R. For the Z-boson this means that $M_R \approx M_Z - 26{MeV}$ and $Γ_R \approx Γ_Z-1.2{MeV}$ where M_Z and $Γ_Z$ are the values reported in the particle data tables.

hep-ph↗

arXiv1999

Relativistic Resonances, Relativistic Gamow Vectors and Representations of the Poincare' Semigroup

The foundations of time asymmetric quantum theory are reviewed and are applied to the construction of relativistic Gamow vectors. Relativistic Gamow vectors are obtained from the resonance pole of the S-matrix and furnish an irreducible representation of the Poincare' semigroup. They have all the properties needed to represent relativistic quasistable particles and can be used to fix the definition of mass and width of relativistic resonances like the Z-boson. Most remarkably, they have only a semigroup time evolution into the forward light cone---expressing time asymmetry on the microphysical level.

hep-th↗

arXiv1998

Quantum Theory in the Rigged Hilbert Space-Irreversibility from Causality

After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket formalism, allows the choice of asymmetric boundary conditions analogous to the retarded solutions of the Maxwell equations for the radiation arrow of time. This led to irreversibility on the microphysical level as exemplified by decaying states or resonances. Resonances are mathematically represented by Gamow kets, functionals over a space of very well-behaved (Hardy class) vectors, which have been chosen by a boundary condition (outgoing for decaying states). Gamow states have all the properties that one heuristically needs for quasistable states. For them a Golden Rule can be derived from the fundamental probabilities that fulfills the time-asymmetry condition which could not be realized in the Hilbert space.

quant-ph↗