If
the
electro-
magnetic
field
is
that
of
a
light
quantum,
the
vacuum
polarization
eSects
are
equivalent
to
ascribing
a
proper
mass
to
the
photon.
Previous
calculations
have
yielded
non-vanishing,
diver-
gent
expressions
for the
light
quantum
proper
mass.
However,
the
latter
quantity
must
be
zero
in
a
proper
gauge
invariant
theory.
The
failure
to
obtain
this
result
from
a
gauge
in-
variant
formulation
can
be
ascribed
only
to
a
faulty
application
of
the
theory,
rather
than
to
an
essential
deficiency
thereof.
When
the
e1ectro-
magnetic
field
is
that
of
a
given
current
dis-
tribution,
one
obtains
a
logarithmically
divergent
contribution
to
the
vacuum
polarization
current
which
is
everywhere
proportional
to
the
given
distribution.
This
divergent
result
expresses
the
possibility,
according
to
present
theory,
of
creat-
ing
electron-positron
pairs
with
unlimited
energy,
a
situation
that
presumably
will
be
corrected
in
a
more
satisfactory
theory.
Thus
the
physically
significant
divergence
arising
from
the
vacuum
polarization
phenomenon
occurs
in
a
factor
that
alters
the
strength
of
all
charges,
a
uniform
renormalization
that
has
no
observable
conse-
quences
other
than
the
conHict
with
the
empirical
finiteness
of
charge.
The
interaction
between
the
electromagnetic
field
vacuum
Ructuations
and
an
electron,
or
more
exactly,
the
electron-positron
matter
field,
modifies
the
properties
of
the
matter
field
and
produces
the
self-energy
of
an
electron.
The
mechanism
here
under
discussion
is
commonly
described
as
the
virtual
emission
and
absorption
of
a
light
quantum
by
an
otherwise
free
electron,
although
an
equally
important
effect
is
the
partial
suppression,
via
the
exclusion
principle,
of
the
coupled
vacuum
Huctuations
of
the
e1ec-
tromagnetic
and
matter
fields.
In
a
Lorentz
invariant
theory,
self-energy
e6'ects
for
a
free
electron
can
only
result
in
the
addition
of
an
electromagnetic
proper
mass
to
the
electron's
mechanical
proper
mass.
Calculations
performed
for
a
stationary
electron'
have
yielded
a
loga-
rithmically
divergent
electromagnetic
proper
mass,
a
divergence
that
results
from
the
possi-
bility
of
emitting
light
quanta
with
unlimited
energy.
It
is
here,
as
in
the
vacuum
polarization
problem,
that
modifications
will
be
introduced
in
a
more
satisfactory
theory.
However,
the
electromagnetic
proper
mass
merely
produces
a
renormalization
of
the
electron
mass
that
has
no
observable
consequences,
other
than
the
conflict
with
the
empirical
finiteness
of
mass.
It
is
evident
that
these
two
phenomena
are
quite
analogous
and
essentially
describe
the
interaction
of
each
held
with
the
vacuum
fluctuations
of
the
other
field.
The
effect
of
these
Auctuation
interactions
is
simply
to
alter
the
fundamental
constants
e
and
m,
although
by
logarithmically
divergent
factors.

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- Fall '05
- Mass, Quantum Field Theory, commutation relations, Julian Schwinger, space-like surface