Schwinger's Source Theory
Mike Mowbray
winner for QED) and came across his "Source Theory" formulation of quantum
field theory. (See for example his books on the subject, which are probably
in any long-established University Physics Library.) I gather that
Schwinger's "Source Theory" formulation never caught on (or failed), as
I've never heard of it anywhere else. But I'm curious about why. - From
what I've read so far, he derives the usual important quantum
electrodynamic effects without requiring any tricky renormalization
techniques, which is pretty neat. (I.e: apparently he didn't have to deal
with unwanted infinities at all.)
I know that some of the examples to which he applied the method are now old
(e.g: there was one example where he treated the pion as the mediator of
the strong interaction), but I get the impression that his method itself
stands separately from any particular application.
Can anybody tell me whether it's a case of:
1) "Schwinger's Source-Theory formulation simply didn't
catch on, but is basically ok as a formalism",
or
2) "There are quantitative reasons why Schwinger's
Source-Theory formulation fails, namely ......." ?
[If anyone does answer, could you please email me direct as well as
posting, as news seems to take quite a while to reach me. Thanks.]
--
Mike Mowbray Email: mi...@nms.otc.com.au
Martin Ouwehand
mi...@nms.otc.com.au (Mike Mowbray) writes:
] I was looking through the works of Julian Schwinger (joint Nobel Prize
] winner for QED) and came across his "Source Theory" formulation of quantum
] field theory. (See for example his books on the subject, which are probably
] in any long-established University Physics Library.) I gather that
] Schwinger's "Source Theory" formulation never caught on (or failed), as
] I've never heard of it anywhere else. But I'm curious about why. - From
] what I've read so far, he derives the usual important quantum
] electrodynamic effects without requiring any tricky renormalization
] techniques, which is pretty neat. (I.e: apparently he didn't have to deal
] with unwanted infinities at all.)
[...]
] Can anybody tell me whether it's a case of:
]
] 1) "Schwinger's Source-Theory formulation simply didn't
] catch on, but is basically ok as a formalism",
] or
] 2) "There are quantitative reasons why Schwinger's
] Source-Theory formulation fails, namely ......." ?
Schwinger is a kind of modern Kepler, he is very "aesthetics driven" :
in developping his theory, he quite often ressorts to arguments that in effect
are along the lines of "wouldn't the universe be nicer and more symmetrical
if we assumed this and this...". In the end, the result is that it is very
difficult to express his theory as a small number of "laws", there is no
real formalism, it is more a kind of philosophy. So I think that his source
theory didn't catch because its formalism is not definite enough.
I vaguely remember however that in his book "Sources, particles and fields"
he somewhere points out a quantitative prediction of his source theory
which disagree with "conventional" QED, but I've never heard that it was
experimentally tested. This is strange because an alternative "contradict
Nobel Prize winner/vindicate an outcast theory" sounds quite attractive
to me :-)
Another approach to QED without infinities I've heard of is G. Scharf's
"Finite quantum electrodynamics". A quick browse in the data base at the
Library of Congress shows that a new edition of this book has just been
published by Springer.
--
Martin
Patrick Labelle
> In article <415c0i$s...@galaxy.ucr.edu>,
> mi...@nms.otc.com.au (Mike Mowbray) writes:
>
> ] I was looking through the works of Julian Schwinger (joint Nobel Prize
> ] winner for QED) and came across his "Source Theory" formulation of quantum
> ] field theory. (See for example his books on the subject, which are probably
> ] in any long-established University Physics Library.) I gather that
> ] Schwinger's "Source Theory" formulation never caught on (or failed), as
> ]
> ] 1) "Schwinger's Source-Theory formulation simply didn't
> ] catch on, but is basically ok as a formalism",
> ] or
> ] 2) "There are quantitative reasons why Schwinger's
> ] Source-Theory formulation fails, namely ......." ?
>
>
> I vaguely remember however that in his book "Sources, particles and fields"
> he somewhere points out a quantitative prediction of his source theory
> which disagree with "conventional" QED, but I've never heard that it was
> experimentally tested. This is strange because an alternative "contradict
> --
> Martin
>
That's very interesting, could someone else answer these questions??
My personal impression was that Schwinger's formalism was equivalent
to "conventional" QED. The reason it did not catch on, I thought, was
simply its complexity. You see, Schwinger was littreally a mathematical
genius (even compared with top rated physicists, he was a class on his
own). He had in fact produced many higher order calculations (which
usually involve divergences) independently, among which the first
calculation of the order alpha correction to the anomalous magnetic
moment of the electron (the famous alpha/2 pi term). Then came
along Feynman, with his Feynman diagrams, and intuitive way of
thinking. Feynman's approach is MUCH simpler than anything Schwinger
ever did in QED. That's why everybody use Feynman's diagrams nowadays
(and path integrals, and Feynman integrations tricks and so on),
because Feynman found a way to do things that could be actually used
by other people, whereas only a Scwhinger could crank out calculations
using his formalism.
SO that's what I was thinking, but now it might seem like his
approach might not be totally equivalent to QED? Or mayve source theory
is not exactly the same thing that Schwinger was using around the
time of the Shelter island conference? (I thought that Dyson had
actually proven the approaches of Schwinger and Feynman to be equivalent..)
Can someone set me straight?
Patrick
lab...@prism.physics.mcgill.ca
Hughan Ross
: On 23 Aug 1995, Martin Ouwehand wrote:
: > I vaguely remember however that in his book "Sources, particles and fields"
: > he somewhere points out a quantitative prediction of his source theory
: > which disagree with "conventional" QED, but I've never heard that it was
: > experimentally tested. This is strange because an alternative "contradict
: That's very interesting, could someone else answer these questions??
: My personal impression was that Schwinger's formalism was equivalent
: to "conventional" QED. The reason it did not catch on, I thought, was
: simply its complexity. You see, Schwinger was littreally a mathematical
: genius (even compared with top rated physicists, he was a class on his
: own). He had in fact produced many higher order calculations (which
[etc]
Schwinger's source theory ideas have found their way into the textbooks
but you don't see people explicitly acknowledge him (much). Schwinger's
approach was basically a differential one as opposed to Feynman's
integral one. Schwinger was the first to propose that Euclidean Green
functions should be easier to play with than their Lorentzian
counterparts. Even path-integral texts use source theory to write the
partition function down in a form where the Green functions pop out by
functional differentiation and then setting the source to zero.
Functional differentiation plus the quantum action principle plus the
equal time commutation relations give you the Schwinger-Dyson
equations---essentially a source theory derivation. So source theory
has been integrated (N.P.I.!) into the theory of quantum fields rather
than forgotten or ignored.
As for Schwinger being "...a mathematical genius...he was a class on his
own).", I have heard it said he was on another branch of the complex
plane but a class on his own is stretching it a bit far. Read Mark
Kac's account of Schwinger's role in solving a problem he had with
Bessel functions. It is in the book:
Mark Kac : probability, number theory, and statistical physics : selected
papers / edited by K. Baclawski and M. D. Donsker
Cambridge, Mass. : MIT Press, c1979
xxxviii, 529 p. ; 26 cm.
(Mathematicians of our time ; 14)
ISBN 262110679
Call No.: q QA 273 .K11 m
The amusing thing is that despite nearly solving the problem completely
he was foiled by a conflict of conventions regarding the sign of an
integral. Mark Kac who was aware of the two conventions spotted the
mistake straight away. Food for thought.
Bye!
Hughan.
No Signature I'm afraid.....
Martin Ouwehand
Patrick Labelle <labelle@/users/labelle> writes:
] SO that's what I was thinking, but now it might seem like his
] approach might not be totally equivalent to QED? Or mayve source theory
] is not exactly the same thing that Schwinger was using around the
] time of the Shelter island conference? (I thought that Dyson had
] actually proven the approaches of Schwinger and Feynman to be equivalent..)
] Can someone set me straight?
Indeed not. He developped source theory during the sixties.
--
Martin
Henrique Fleming {F}
[Mod. Note: Stuff deleted to make posting shorter. crb]
: Patrick Labelle (labelle@/users/labelle) wrote:
: but you don't see people explicitly acknowledge him (much). Schwinger's
: approach was basically a differential one as opposed to Feynman's
: integral one. Schwinger was the first to propose that Euclidean Green
: functions should be easier to play with than their Lorentzian
: counterparts. Even path-integral texts use source theory to write the
: partition function down in a form where the Green functions pop out by
: functional differentiation and then setting the source to zero.
: Functional differentiation plus the quantum action principle plus the
: equal time commutation relations give you the Schwinger-Dyson
: equations---essentially a source theory derivation. So source theory
: has been integrated (N.P.I.!) into the theory of quantum fields rather
: than forgotten or ignored.
: As for Schwinger being "...a mathematical genius...he was a class on his
: own).", I have heard it said he was on another branch of the complex
: plane but a class on his own is stretching it a bit far. Read Mark
: Kac's account of Schwinger's role in solving a problem he had with
: Bessel functions. It is in the book:
...
: The amusing thing is that despite nearly solving the problem completely
: he was foiled by a conflict of conventions regarding the sign of an
: integral. Mark Kac who was aware of the two conventions spotted the
: mistake straight away. Food for thought.
: Hughan.
Well, the Source Theory which occupied Schwinger in his last
years is much more radical than functional differentiation.
In it "Euclidicity" is used as a dynamical principle. You
require of your theory that every expression is meaningful
also in Euclidean metric (e.g. no preferred axis is allowed).
He calls that space-time uniformity. I quote:
"We have seen causality and space-time uniformity working as
creative principles. The physical requirement of completeness,
or unitarity, has then be verified;it is not an independent
principle." (Schwinger, "Particles, Sources and Fields",
Vol.1, pg.59). As for
As for the result that turns out to be different from
"conventional" QED, it's in Vol.3. It is the photon
decay of the neutral pion. Obviously it is not a
pure QED problem.
--
Henrique Fleming | La duda, una de las formas
fle...@snfma1.if.usp.br | de la inteligencia...
Sao Paulo,Brazil | J.L.Borges
-------------------------------------------------------
Jack Sarfatti
>
>Well, the Source Theory which occupied Schwinger in his last
>years is much more radical than functional differentiation.
>In it "Euclidicity" is used as a dynamical principle. You
>require of your theory that every expression is meaningful
>also in Euclidean metric (e.g. no preferred axis is allowed).
>He calls that space-time uniformity. I quote:
>"We have seen causality and space-time uniformity working as
>creative principles. The physical requirement of completeness,
>or unitarity, has then be verified;it is not an independent
>principle." (Schwinger, "Particles, Sources and Fields",
>Vol.1, pg.59). As for
>
This is puzzling. If we go to the Euclidean case there is no more
causal light cone structure. So how does he get causality from
space-time uniformity? It's like getting "causality without causality".
Are you also saying that Schwinger derived both causality and unitarity
from the single idea of "Euclidicity". I like that because it means
that if causality is violated then so is unitarity and vice versa.
That seems sort of correct since it can be shown that it is the
unitarity of quantum mechanics which prevents the violation of
causality by signals using quantum nonlocal connections. Is
Schwinger's result merely another way of doing Eberhard's theorem?
--
http://www.hia.com/hia/pcr
John E. Davis
: Well, the Source Theory which occupied Schwinger in his last
: years is much more radical than functional differentiation.
[Gosh, I cannot believe that I missed this thread. Since at least one
person has confused Schwinger's Green function approach which Schwinger
developed in the late 40s with his source theory of the 60s, hopefully, I
have not missed too much.]
Unfortunately I have never had the time to sit down and learn source theory.
It seems that there are only a few people who understand it at all despite
Schwinger's claim that it is free of the infinities that plague QED. As I
recall, Schwinger says that he hit upon source theory while teaching Quantum
Mecahnics at Harvard. Apparantly he had been thinking about some way to do
away with q-numbers and express QM entirely as c-numbers--- source theory
was the result. Unfortunately none of his ideas on the matter were taken
very seriously at Harvard and so he eventually moved to UCLA. Does anyone
know if his ideas were received any better there?
How does source theory fit in with gauge theories in general?
: As for the result that turns out to be different from
: "conventional" QED, it's in Vol.3. It is the photon
: decay of the neutral pion. Obviously it is not a
: pure QED problem.
Is there any experimental evidence that helps distinguish QED from source
theory?
Has anyone else written anything more readable on the subject than
Schwinger? (Does anyone other than Schwinger understand it?).
--John