**REINHARD OEHME**

**A FEW PUBLICATIONS WITH COMMENTS**

·
**ERZEUGUNG VON PHOTONEN BEIM ZUSAMMENSTOSS VON
NUKLEONEN**

R. Oehme

Z. Physik
129, 573 (1951)

(Doctoral Thesis, Goettingen, as student of Werner
Heisenberg);

·
**PI-MESONEN UND GAMMA-STRAHLUNG**

R. Oehme

in Kosmische
Strahlung, edited by W. Heisenberg, (Springer-Verlag,
Berlin, 1953) p. 132.

In these papers I explore all aspects of the production of photons in high energy collisions of nucleons.

The results are of considerable interest for the understanding of cosmic radiation.

·
**PI-MESONEN UND QUANTISIERTE FELDTHEORIEN**

Gerhard Lueders, Reinhard Oehme and Walter E. Thirring

in Heisenberg Festschrift, Z. Naturforschung
7a, 213 (1952).

Survey and general assessment of strong interactions within the framework of the status of quantum

field theory of the day.

° DISPERSION RELATIONS FOR THE SCATTERING OF CHARGED MESONS

Reinhard Oehme

Results presented at the Institute for Nuclear Studies in the Winter Quarter

1954/55, and published in the papers listed below.

I discovered that for scattering amplitudes of massive particles with charges, the crossed channel

branch cuts in the complex energy plane are due to the absorptive parts (cross

sections) of the amplitudes with CHARGE CONJUGATE projectals.

Hence the corresponding dispersion relations are NOT simple analogues of the

Kramers-Kronig Relations for photons, as had been proposed.

Furthermore, in the presence of intermediate states with energies below the

physical threshold, the derivation of the required analytic properties can

become a non-trivial problem which I was the first to resolve. I discussed these matters

often with Hironari Miyazawa.

It was my work in 1954/55 which produced the first correct hadronic dispersion

relations and provided an understanding of their mathematical background.

I obtained the proper CROSSING RELATIONS, which make the connection

with perturbation theory, and which were to play an important role in further

developments, including meromorphic models and Regge theory.

·
**APPLICATION OF DISPERSION RELATIONS TO
PION-NUCLEON SCATTERING**

M. L. Goldberger, H. Miyazawa and R. Oehme

Phys. Rev. 99, 986 (1955);

·
**DISPERSION RELATIONS FOR PION-NUCLEON
SCATTERING**

R. Oehme

Phys. Rev. 100, 1503 (1955), and 102, 1174 (1956);

·
**DISPERSION RELATIONS FOR NUCLEON-NUCLEON
SCATTERING**

·
M.L. Goldberger, R. Oehme
and Y. Nambu

Ann.Phys.
(N.Y.) 2, 226 (1956).

As mentioned above, for the
scattering of massive particles with charges, we noted that the

crossed channel branch cuts in the complex energy plane are due to the absorptive parts

(cross
sections) of the amplitudes with **charge conjugate projectals**.
With this input, we

obtain the complete dispersion relations for the scattering of charged pions on protons. These

relations
are found to be in good agreement with experimental results (Fermi, Lindenbaum).

We present the GMO-Sum Rules for the difference of particle-particle and
antiparticle-particle

amplitudes. These are the first superconvergence relations. At zero energy, they express the

scattering
length in terms of integrals over total cross sections.

In contrast to
photon scattering,

where the analytic properties of the amplitude can be directly read off from the representation

as the Fourier transform of a retarded product, more sophisticated methods are required for

the
scattering of massive particles.

The FIRST proof of relativistic
dispersion relations for

massive
particles is given in the appendix to my paper in Il Nuovo
Cimento 4, 1316 (1956).

In the second paper quoted above, I also discussed possible modifications of
dispersion relations

in case there should be violations of local commutativity.

·
**CHARGE CONJUGATION NON-CONSERVATION**

R. Oehme

Letter to C.N. Yang dated August 7, 1956.

Reprinted in *Selected Papers 1945-1980* , by Chen Ning
Yang

(W.H. Freeman and Co., San Francisco, New York, 1983) p. 32.

In this letter, I present my direct calculation providing the proof of

**Charge Conjugation
Non-Conservation**

in the event of a positive outcome of the polarization experiment in beta-decay. Since Parity

conservation leads to the same restrictions, I point out that C and P must BOTH be violated

in order to get an asymmetry.

Since it involves the exchange of matter and anti-matter, I consider the
non-conservation of C

to be a fundamental result with far reaching consequences. Taken together, C- and P-violation

were setting the stage for the later CP experiments and their fundamental results, which are

at a lower level of the interaction strength.

(In connection with my letter, the following should be noted: the preprint BNL 2819 of the

Nobel paper on parity non-conservation in weak interactions contains the statement that

C is PRESERVED in weak interactions. [The reason given is the equality of lifetimes of mesons

with opposite charges]. The final version of the paper was published after the receipt of my

letter of August 7, and my communication is acknowledged in the article. The content of my

letter is NOT mentioned, but the original remarks about C-conservation are removed.

A reprint of my communication is contained in the 1983 publication of C.N. Yang quoted above.

It should be noted that, when I
wrote this letter in

Institute for Advanced Study in

·
**REMARKS ON POSSIBLE NON-INVARIANCE UNDER TIME
REVERSAL AND **

** CHARGE CONJUGATION.**

T.D. Lee, R. Oehme and C. N. Yang

Phys.
Rev. 106, 340 (1957).

Reprinted in Selected Papers 1945-1980, by Chen Ning Yang (W.H. Freeman and Co.,

pp. 8-13; and in HEP(USPIRES-SLAC, Oehme, R.).

The idea of this paper originates from my letter to C.N. Yang on August 7,
1956, which first raised

the questions of C and T non-conservation in the context of P violation. In particular, it was shown

in this letter that the C-invariance must be violated in the proposed $\beta$-decay experiments for

the detection of P non-invariance. The paper gives a detailed discussion of the interplay of the possible

non-invariance under P, C and T, and of applications to the K - anti-K complex. It is of fundamental

importance for the discussion of CP non-invariance, which was discovered later.

·
**CAUSALITY AND DISPERSION RELATIONS FOR THE
SCATTERING OF MESONS **

** BY FIXED
NUCLEONS**

R. Oehme

Il
Nuovo Cimento 4,
1316 (1956).

In spite of its title, this paper gives the basic idea for the proof of forward dispersion relations: the

``gap method''. The appendix contains the FIRST EXACT PROOF of relativistic forward dispersion

relations for hadron-hadron scattering. The proof is given for pi-pi scattering; but the extension to

pi-N scattering is straightforward if the gap method is also used for the pi-N vertex.

·
**PROOF OF DISPERSION RELATIONS AND THE EDGE OF
THE WEDGE THEOREM**

Reinhard Oehme

Colloquium presented at Palmer Hall,

·
**UNE DEMONSTRATION POSSIBLE DES RELATIONS DE
DISPERSION**

H. J. Bremermann, R. Oehme
and J. G. Taylor

presented at Les Problemes Mathematiques
de la Theorie Quantique des
Champs,

Colloques Internationaox du CNRS,

Internationaux du Centre National de la Recherche Scientifique, LXXV, 169 (1959);

·
**PROOF OF DISPERSION RELATIONS IN QUANTIZED
FIELD THEORIES **

**(Edge of the Wedge Theorem)**

H. J. Bremermann, R. Oehme and J. G. Taylor

Phys. Rev. 109, 2178 (1958).

We formulated and proved what I called the EDGE OF THE WEDGE THEOREM

("Keilkanten Theorem"). By now, it is considered a fundamental theorem in the theory of

several complex variables, and it has been used in many applications. The theorem provides

an enlargement of the initial domain of analyticity, which then can be used for the construction

of
envelopes of holomorphy.

Our proof of the theorem is as general as is required for dispersion relations,
and it

can be adapted to distribution-valued boundaries. (With certain restrictive assumptions,

one can
give simplified proofs (see, for instance, F.J. Dyson, Phys. Rev. 110,
1460 (1958)).

Using the results from the Edge of the Wedge Theorem for the analytic
properties of

scattering amplitudes, we apply the powerful geometrical tools of the theory of several

complex
variables in order to obtain **envelopes of holomorphy**.
The resulting regions

of analyticity are then used for the construction and proof of non-forward dispersion

relations. This is the first time the geometrical methods of analytic completion were used

in field theory.

The Edge of the Wedge theorem, together with the methods of analytic
completion, are also

of considerable interest for theories with broken Lorentz invariance. The theorem is the basis

for a proof that microcausality, and non-negative energy in all frames, imply the standard,

invariant energy-momentum relations, even if Lorentz invariance is violated otherwise.

·
**VERTEX FUNCTIONS IN QUANTISED FIELD THEORIES**

R. Oehme

Phys. Rev. 111, 1430
(1958);

·
**THE COMPOUND STRUCTURE OF ELEMENTARY
PARTICLES**

R. Oehme

in Werner Heisenberg und die Physik unserer Zeit, Festschrift, (Verlag
Friedrich

·
Vieweg und Sohn,

Non-perturbative "Anomalous Thresholds" are discovered, and an interpretation is given in terms

of the structure of particles as composite systems of other particles. I prove that these "Structure

Singularities" are related to absorptive thresholds of connected amplitudes. For sufficiently tight

binding, these thresholds appear in the continuation into secondary Riemann sheets through the

absorptive cuts of the original Green's function. With decreasing binding, they move into the

physical Riemann sheet.

·
**COMPLEX ANGULAR MOMENTUM IN RELATIVISTIC
DISPERSION THEORY**

R. Oehme and G. Tiktopoulos

Phys. Lett. 2, 86 (1962);

·
**MOVING POLES AND ELEMENTARY PARTICLES**

R. Oehme

Phys. Rev. Lett. 9, 358 (1962);

·
**HIGH ENERGY SCATTERING AND RELATIVISTIC
DISPERSION THEORY**

R. Oehme

Ravenna Lectures, in Dispersion Relations and their Connection with
Causality ,

· edited by E. P. Wigner (Academic Press, New York 1964) pp. 167-256;

·
**FIXED POLES IN THE COMPLEX ANGULAR MOMENTUM
PLANE **

R. Oehme

Phys. Rev. Lett. 18, 1222 (1967).

Complex Angular Momentum and Regge Singularities are obtained
within the framework of relativistic

dispersion theory, and hence of field theory. (Regge considered Schroedinger theory, and most other

discussions used heuristic methods). Exact t-channel unitarity constraints on Regge surfaces and their

implications are
discussed.

A proof is given that the Pomeron
cannot be fixed pole without shielding

branch cuts.

·
**SPURION THEORY OF BROKEN U_L(12)
SYMMETRY**

R. Oehme

Phys. Rev. Lett. 14, 664 (1965);

·
**BREAKING OF UL(12)
SYMMETRY**

R. Oehme

Phys. Rev. Lett. 14, 866 (1965);

·
**A LORENTZ COVARIANT SUPERMULTIPLET SCHEME**

R. Oehme

in High Energy Physics and Elementary Particles (IAEA, Vienna,
1965) pp. 533-548.

Independent introduction of collinear SU(6),
SU(3)XSU(3), etc., and applications in model building.

·
**BROKEN SYMMETRIES AND LEPTONIC WEAK
INTERACTIONS**

R. Oehme

Ann. of Physics (N.Y.) 33, 108 (1965);

·
**CURRENT ALGEBRA AND THE SUPPRESSION OF
LEPTONIC **

·
**MESON-DECAYS WITH Delta \S\ = 1 **

R. Oehme

Phys. Rev. Lett. 16, 215 (1966).

The first paper contains already a hard meson version of what has later come to be

called the Callan-Treiman relation, see ref.1 of the 2nd paper.

·
**FORWARD DISPERSION RELATIONS AND MICRO-
CAUSALITY **

R. Oehme

in Quanta , Wentzel
Festschrift (Univ. of Chicago Press, Chicago, 1970) pp. 309-337.

After a survey of the status of forward dispersion relations, we return here to
a discussion of the

changes which may result from possible VIOLATIONS OF MICRO-CAUSALITY (local

commutativity). These violations are considered with and without Lorentz invariance.

·
**RISING CROSS SECTIONS **

R. Oehme

Springer Tracts in Modern Physics
61, 109 (1972).

Text of a lecture given in
July 1971 at DESY, before rising cross sections were experimentally

discovered. From our previous studies of allowed leading singularities in the complex angular

momentum plane, we argue that the most natural singular structures would lead to rising cross

sections.

·
**ASYMPTOTIC FREEDOM AND HIGH ENERGY SCATTERING**

·
** **

R.
Oehme

in Proceedings of the International
Symposium on Mathematical Physics,

·

·
**ASYMPTOTIC FREEDOM, POTENTIAL SCATTERING AND
HIGH ENERGY LIMITS**

D. Heckathorn and R. Oehme

Phys. Rev. D 13, 1003 (1976).

Existence of new ``short-distance'' Regge singularities due to gluonic interactions; their relevance for

the bare Pomeron, (see also the thesis of D. Heckathorn, Phys. Rev. D 18, 1286 (1978)).

·
**QUARK AND GLUON PROPAGATORS IN QUANTUM
CHROMODYNAMICS**

R. Oehme and W. Zimmermann

Phys. Rev. D 21,
471 (1980); SPIRES-HEP Oehme, R;

·
**GAUGE FIELD PROPAGATOR AND THE NUMBER OF
FERMION FIELDS **

R. Oehme and W. Zimmermann

Phys. Rev. D 21, 1661 (1980); SPIRES-HEP Oehme,
R;

·
**ON SUPERCONVERGENCE RELATIONS IN QUANTUM
CHROMODYNAMICS **

R. Oehme

Phys. Lett. B 52, 641 (1990).

For gauge theories with confinement, we show that there generally exist branch
cuts in colored channels.

The branch points
move to infinity only as the coupling parameter approaches an infrared-stable
fixed point.

We discover superconvergence relations for gauge field
propagators and present an exact structure analysis.

Superconvergence relations exist only if the number of matter fields (flavors) is below a given limit. The

relations provide a link between long- and short-distance properties of the theory. They are of

importance for confinement.

·
**REDUCTION AND REPARAMETRIZATION OF QUANTUM
FIELD THEORIES**

R. Oehme

Nambu Festschrift, Progress of Theoretical
Physics, Supplement, 86, 215 (1986);

· CERN-Report TH. 42-45/85; SPIRES-HEP Oehme, R. ;

·
**RELATIONS BETWEEN EFFECTIVE COUPLINGS FOR
ASYMPTOTICALLY **

·
**FREE MODELS**

R. Oehme and W. Zimmermann

Max Planck Inst. Report MPI-PAE/PTh 60/82, SLAC
Spires 84, Oehme, R; Comm.

· Math. Phys. 97, 569 (1985).

·
**REDUCTION OF COUPLING PARAMETERS AND DUALITY **

R. Oehme

in Recent Developments in Quantum Field Theory, Springer Verlag, Heidelberg, New York.

·
Talk given at the Ringberg
Symposium on Quantum Field Theory,

· 21-24 Jun 1998. Lecture Notes in Physics 558:136-156, (2000); EFI-99-01,

· MPI-PH-99-04, hep-th/9903092.

As a general method of imposing restrictions on quantum field theories with several parameters,

we have introduced a theory of reduction of couplings. This method is based upon the renormalization

group, and is more general than the imposition of symmetries. There are solutions of the reduction

equations which do not correspond to additional symmetries, but may be related to aspects of superstring

theories. Our reduction theory is finding a wide range of applications.

·
**CONSTRUCTION OF GAUGE FIELD THEORIES WITH A
SINGLE COUPLING **

·
**PARAMETER FOR YANG-MILLS AND MATTER FIELDS **

R. Oehme, K. Sibold and W.
Zimmermann

Phys. Lett. B 153, 142 (1985);
SPIRES-HEP Oehme, R.

·
**RENORMALIZATION GROUP EQUATIONS WITH
VANISHING LOWEST **

·
**ORDER OF THE PRIMARY BETA-FUNCTION**

R. Oehme, K. Sibold and W.
Zimmermann

Phys. Lett. B 147, 115
(1984); SPIRES-HEP Oehme, R.

·
**REDUCTION OF DUAL THEORIES**

R. Oehme

Phys. Rev. D 59, 0850 (1999). hep-th/9808054.

Some
characteristic applications of our coupling parameter reduction scheme.

·
**ANALYTIC STRUCTURE OF AMPLITUDES IN GAUGE
THEORIES **

·
**WITH CONFINEMENT**

·
R. Oehme

(Invited
Talk presented at the International Congress of Mathematical Physics, Paris,
July 1994);

·
Report MPI-Ph/94-52, hep-th/9412024;

Intern.
J. of Mod. Phys. A10 (1995) 1995;

·
**SINGULARITIES OF HADRONIC AMPLITUDES IN
QUANTUM CHROMODYNAMICS**

·
R. Oehme

Mod.
Phys. Lett. 8, 1533 (1993);

·
**DISPERSION RELATIONS IN GAUGE THEORIES WITH
CONFINEMENT**

·
R. Oehme

(Plenary
talk at the XVIIIth International Workshop on High
Energy Physics and Field

·
Theory, June 1995,

in Quanta-Relativity-Gravitation,
Proceedings,

·
(State Research Center of Russia, Protvino, 1996), pp. 275-282; hep-th/9511006.

On the basis of my earlier
results on structure singularies of amplitudes, I
discuss the analytic properties

of physical (hadronic) and of unphysical amplitudes in theories with confinement. In all Riemann sheets

of physical amplitudes, there are no structure singularities due to the quark structure.

·
**GLUON CONFINEMENT**

R. Oehme

Phys. Lett.
B 195}, 60 (1987);

·
**RENORMALIZATION GROUP, BRST COHOMOLOGY, AND
THE **

·
**PROBLEM OF CONFINEMENT**

R. Oehme

Phys. Rev. D 42, 4209 (1990);

·
**SUPERCONVERGENT GLUON PROPAGATOR AND THE **

·
**QUARK-ANTIQUARK POTENTIAL**

R. Oehme

Phys. Lett.
B 232, 498 (1989).

Using superconvergence relations, general arguments are given for gluon confinement and for an

approximately linear quark/antiquark-potential for QCD with less than ten flavors.

·
**SUPERCONVERGENCE, SUPERSYMMETRY AND CONFORMAL
INVARIANCE **

R. Oehme

in Leite Lopes Festschrift,
edited by N. Fleury, S. Joffily,
J. A. M. Simoes and A. Troper

· (World Scientific Publishing Co., Singapore, London, 1988), p. 443-458; SPIRES-HEP

· Oehme, R. ;

·
**SUPERCONVERGENCE, CONFINEMENT AND DUALITY **

(Talk presented at the International Workshop on High Energy Physics, Novy Svet,

·

· (Bogoliubov Institute, Kiev, 1995) pp. 107-116; EFI 95-45, MPI-Ph/95-102, hep-th/9511014.

·
**DUALITY, SUPERCONVERGENCE AND THE PHASES OF
GAUGE THEORIES **

R. Oehme

Phys. Lett. B 232, 67 (1997);
hep-th/9701012.

I apply the superconvergence relations to the problem
of confinement in N=1 Supersymmetric

Gauge Theories with the number of flavors below a specific limit. My results agree with those

derived more recently from Seiberg-Witten Duality, in particular in connection with the existence

of the Coulomb Phase. Actually, my conclusions are already given in the Lopez Festschrift of 1988.

In contrast to duality, my methods are applicable to non-SUSY theories.

·
**EDGE OF THE WEDGE THEOREM, MICROCAUSALITY AND
LORENTZ NON-INVARIANCE**

Reinhard Oehme

X Mexican School on Particles and Fields, Playa del Carmen, Mexico, 2002.

·

In connection with possible space-time non-commutativity,
field theories with violations of Lorentz invariance

· of interest. Using the Edge of the Wedge theorem, which I discovered and proved in 1956 in collaboration

· with H. L. Bremermann and J. G. Taylor, together with analytic completion, one can show that

· microcausality (plus energy positivity) implies Lorentz invariant boundaries of spectral contributions for

· Green's functions in momentum space (e.g. Borchers, Ann. Henri Poincare 3, 1 (2002), and references given there ).

· REDUCTION OF QUANTUM FIELD THEORIES

Reinhard Oehme and Wolfhart Zimmermann

(in preparation)