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 Chicago, I already had an appointment at the

Institute for Advanced Study in Princeton)

· 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., San Francisco,

New York, 1983) p.199; in CP-Violation, edited by L. Wolfenstein, (North Holland, Amsterdam, 1989)

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, Princeton University, Winter 1956/57;

· 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, Lille, France, 3-8 Juin 1957, printed in Colloques

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, Braunschweig, Germany 1961), p.240.

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,

· Mexico City, January 1976 (I.P.N., Mexico, 1976) pp. 555-583;

· 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, Ringberg Castle, Tegernsee,

· 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, Moscow-Protvino, Russia)},
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,

· Crimea, September 1995), Proceedings, edited by G.V. Bugrij and L. Jenkovsky

· (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

Oxford University Press or Physics Reports

(in preparation)