* Idea: An expression for the product ea+b = ea eb
n =
2infty
ec_n for non-commuting a and b.@ References: Sridhar & Jagannathan mp/02 [q-analog]; Scholz & Weyrauch JMP(06)mp [calculation of cn].
Topics, Z
Z Particle > see electroweak theory.
Zassenhaus Formula > s.a. path
integrals.
* Idea: An expression
for the product ea+b = ea eb n =
2infty
ec_n for non-commuting a and b.
@ References: Sridhar & Jagannathan mp/02 [q-analog];
Scholz & Weyrauch JMP(06)mp [calculation
of cn].
Zeeman Effect > see atomic physics.
Zeeman Topology > see spacetime topology.
Zeno Effect (In quantum theory; including anti-Zeno effect)
Zeno's Paradox > see logic.
Zermelo's Axiom of Choice > see choice.
Zero
* History: Introduced
by the Babylonians as a placeholder for a blank tablet entry; Explored by Indian
and Muslim cultures, which did not have prejudices
against representing "nothing"; Incorporated in Western thought
using limits and the physics of empty space.
@ History: Kaplan 99, Seife 00 [I].
Zero Divisor > see ring.
Zero Modes > see operators.
Zero-Point Energy, Fluctuations > see vacuum.
Zeta Function > s.a. regularization; series.
$ Def: The most common
one is the Riemann zeta function,
(x):=
n =
1infty n–x
, or (x)
= 
(x)–1 
0infty du ux–1/(eu–1)
.
* History: 1974, H Montgomery
found the first indication of a connection between the distribution of the
zeros of the Riemann -function
and the distribution
of the eigenvalues of random matrices; 1981, Numerical calculations
by A Odlyzko
of statistics of the zeros led to graphs illustrating the connection
that Montgomery predicted.
* Properties: The summation
in the definition is divergent for Re(x)
1, and defined
by analytic continuation; It has a simple pole at x =
1, and no other singularities.
@ General references: Titchmarsh 30; Elizalde JPA(97)ht/96 [singularity
structure]; Katz & Sarnak BAMS(99)
[zeros and symmetry]; Bogomolny et al JPA(06)
[spacing distribution of zeros]; Tyagi & Holm mp/07 [new
integral representation for 0 < Re(x) < 1]; Kuznetsov PRS(07)
[generalization of Riemann-Siegel asymptotic formula]; Kirsten et al JPA(08)-a0812 [meromorphic
properties].
@ Special properties: Berry PRS(95)
[on the critical line x = 
+
it]; Fujii & Suzuki a0805 [(2n+1)
in terms of {(2k)
| k 
1}].
@ Zeros of zeta function and quantum mechanics: Sierra NJP(08)-a0712.
@ Hurwitz zeta function: Espinosa & Moll TRJ(02)m.CA/00 [integrals];
> s.a. Stieltjes Constants, thermodynamical
systems.
@ Other zeta functions: Cacciatori a0902 [polynomial].
Zeta Matrix > see types of posets.
Zitterbewegung [> s.a. dirac
quantum field theory]; spinning particles.
* Idea: An
oscillatory motion with frequency 2H/
,
superimposed on the average translational motion, obtained for a Dirac particle
when using
the usual position operator x (as opposed to the Foldy-Wouthuysen
representation).
@ General references: Schrödinger SBAW(30);
Lock AJP(84)mar;
Hestenes FP(90)
[and interpretation of quantum mechanics], FP(93)
[modeling]; Ghose et al PLA(03)qp [not
found
for
bosons];
Bolte & Glaser
JPA(04)qp [and
semiclassical
observables]; Krekora et al PRL(04)
[no effect for electrons]; Brovetto et al qp/05 [e size
and mass]; Sidharth IJTP(09);
Singh & Mobed CQG(09)-a0903 [effect
of spacetime curvature]; David & Cserti a0909 [general theory].
@ And spacetime algebra: Dreisigmeyer et al FPL(03)qp/01; Hestenes a0802 [model].
@ For photons: Kobe PLA(99);
Wang
et al PRA(09)-a0905.
Zoll, Zollfrei Metric > see types of metrics.
Zorn's Lemma > see axiom of choice.
Zweig Rule
* Idea: The phenomenological
rule according to which strong processes in which the final states can only
be reached through quark-antiquark annihilation
are suppressed.
* Example: The 
(
s s-bar)
decay into 3
is
suppressed wrt decay into 2K.
@ Proposals: Zweig pr(64); Okubo PL(63);
Iizuka PTP(66),
PTP(66).
main page – abbreviations – journals – comments – other
sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified
8 oct 2009