From: terry@aslws01.asl.dl.nec.com (Terry Bollinger)
Subject: Re: Vector Bosons?
Organization: NEC America, Inc. Irving, Texas
Date: Thu, 13 Aug 1992 17:29:44 GMT

In article <d==y5bh@rpi.edu> caer@iear.arts.rpi.edu (Charlie Figura) writes:

> Can someone explain to me what is meant by the term 'vector boson',
> and give examples?  The textbooks I found were all graduate level...

Volume III of the Feynman Lectures on Physics has a pretty decent explanation
of both bosons in general and vector bosons in particular.  He also explains
how the term "vector" came to be used for bosons that have one unit of spin.


   FURTHER ELABORATIONS FOR THE BENEFIT OF INTERESTED NON-PHYSICISTS

BOSONS

For whatever it's worth, a boson is simply a particle with integral spin
(spin = {..,-2,-1,0,1,2,..} ), and fermions are particles whose spins
contain half-unit (spin = { -1 1/2, -1/2, +1/2, +1 1/2 } ).  The idea of
spin does in fact correspond to the idea of angular momentum (spin) of
large scale objects, but at the quantum level it gets sufficiently weird
that spin is usually best thought of as a property (quantum number) with
certain effects on wavefunctions, rather than as "spin" in the conventional
sense.  The units of particle spin are based on Planck's constant.

In all observed cases, bosons states are "commutative" -- meaning more-or-
less that when all the math has been said and done, bosons really like to
be in the same spot at the same time, doing the same thing.  Moreover, the
bigger the party is (that is, the larger the number of bosons "doing the
same thing" becomes -- see Feynman III for details), the more attractive
that "state" becomes to other bosons of that type.  Bosons thus are a most
gregarious bunch, true party animals -- except that their parties tend
towards the dull side, what with *everyone* doing exactly the same thing.

Effects at the everyday level?  Plenty.  Fundamental bosons such as photons
and gluons have no inhibitions about being in the same spot in space, so
that they have no concept of "volume."  For example, how many photons can
you put into a light beam?  Well, because photons are elementary bosons
(that is, they lack any smaller constituent particles), you can pretty
well just keep stuffing them (increasing the beam intensity) ad infinitum.

Einstein first noted the joining-in effect, and lasers were predicted as
one consequence -- a potential photon from an excited atom just cannot
resist joining a mob of identical photons cruising by, and decides to
join in.  Net result?  A burst of coherent (all-in-the-same-state) photons.

With composite bosons -- e.g., complex, multi-particle atoms of helium whose
net spin is a whole number -- it gets a tad more complex, because such atoms
still occupy space.  But the bizarre behavior of superfluid liquid helium
is still very much a reflection of the party-animal (commutative) theme of
all bosons.  Superfluid helium behaves as it does because ALL of its He
atoms are described by the SAME wavefunction -- that is, they're all goin'
to the same party, and once in, they try very hard to STAY there.  Some of
the most conspicuous effects of superfluid helium, such as the disappearance
of He bubbles that boil off constantly in ordinary liquid helium, are a
direct result of this quantum tendency to stay in the same state -- the
liquid dissipates heat collectively, rather than through the "sacrifice"
of individual He atoms through a local event such as the formation of
a bubble during boiling.

In quantum field theory, the gregarious (commutative) behavior of bosons
leads to another interesting effect.  It implies that "virtual" bosons
become the mediators of the various forces that hold things together --
e.g., virtual photons mediate the electromagnetic force, virtual W
particles help mediate the weak force, and gluons mediate the strong
force between quarks.


VECTOR BOSONS

Vector bosons are simply bosons with a spin of 1.  Particles with a spin
of 1 unit can simultaneously have three separate components of what their
spin orientation is, all at the same time.  Objects on that scale tend
to be a bit fuzzy about who or what they really are, until you poke them
really hard and force them to decide.  It's sort of like being able to
be a Hari-Krishna/ Baptist/agnostic UNTIL someone forces you to be more
specific by "measuring" your theological orientation.

In Feynman's explanation, the term "vector" just means that the current
state of particles (bosons) with 1 unit of spin can be represented by an
arrow (vector) pointing somewhere in a three-dimensional space.  The state
of other types of bosons -- e.g., spin 2 bosons -- cannot be represented
with the same simple arrow-pointing-in-space vector representation, and
thus are not called "vector" bosons.


FERMIONS

If you're an elementary particle and you're not a boson, then you have to
be a fermion.  Fermions are contrary cusses that are "anticommutative" --
meaning when all is said and done that that like to have a little elbow
room.  In contrast to the bosons, they most definitely do NOT like to be
in exactly the same spots doing exactly the same thing at the same time,
and will take extraordiary measures to avoid doing so.

Having fermions around is a major factor in why you, the reader, are not
currently part of a little grape-sized black hole orbiting where the earth
used to be.  Fermions in general and atomic electrons (spin 1/2 fermions)
in particular will strongly resist any compression beyond a certain point,
making the volume-occupying properties of ordinary matter possible.

Just as importantly, the WAY ferions resist compression is complex enough
to lead to all sorts of interesting "features" in atoms -- features that
lead directly to what we call chemistry.  Recall the octet of electrons that
form a "complete" shell in chemistry?  That number eight is a direct result
of the electrons using their other quantum number to twist and squirm about
until they can manage to cram eight of themselves into a single roughly
spherical energy level -- a sort of quantum version of the old students-in-
the-phone-booth trick.  But try to add ONE MORE electron to the phone booth
and all the eight others will have a mutual conniption fit, resulting in
them kicking the the poor fellow out into a higher, costlier energy level.

So the poor guy [girl] is left standing out there, all ticked off and surly
and wishing he [she] could just get OUT of that stupid lithium, sodium,
potassium, cesium, actinium atom when along come some hot babes [hunks] in
a little chlorine number with only SEVEN in the car and a low-energy seat
just WAITING to be filled by some lonely fella [gal].  Sparks will fly!

[To any picky physicists:  Yes, I DO know that it's really all one wave-
function and that the electrons cannot truly be distinguished from each
other in the above fashion.  And yes, I'm being sloppy -- but by choice.]

Anyway, back to the main topic:  Complexity in the way fermions work out
there differences, like the resistance itself, is critical to the world
as we know it.  If electrons resisted compression merely by "balooning out"
in some rather dull, uncomplicated way, YOU, dear reader, would be nothing
more than part of an immensely dull soup of multi-element gasses compressed
to roughly liquid form by their collective gravity.  A bit more interesting
than being part of a grape-sized black hole, perhaps... but not by much!


				Cheers & hows that for overkill,
				Terry Bollinger

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| Terry Bollinger                            | Phone: 214-518-3538           |
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