A FEW PUBLICATIONS WITH COMMENTS
ERZEUGUNG VON PHOTONEN BEIM ZUSAMMENSTOSS VON
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
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
M. L. Goldberger, H. Miyazawa and R. Oehme
Phys. Rev. 99, 986 (1955);
DISPERSION RELATIONS FOR PION-NUCLEON
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
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
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
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
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
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
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,
give simplified proofs (see, for instance, F.J. Dyson, Phys. Rev. 110,
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
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
R. Oehme and G. Tiktopoulos
Phys. Lett. 2, 86 (1962);
MOVING POLES AND ELEMENTARY PARTICLES
Phys. Rev. Lett. 9, 358 (1962);
HIGH ENERGY SCATTERING AND RELATIVISTIC
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
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
SPURION THEORY OF BROKEN U_L(12)
Phys. Rev. Lett. 14, 664 (1965);
BREAKING OF UL(12)
Phys. Rev. Lett. 14, 866 (1965);
A LORENTZ COVARIANT SUPERMULTIPLET SCHEME
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
Ann. of Physics (N.Y.) 33, 108 (1965);
· CURRENT ALGEBRA AND THE SUPPRESSION OF LEPTONIC
MESON-DECAYS WITH Delta \S\ = 1
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-
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
· 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
R. Oehme and W. Zimmermann Phys. Rev. D 21, 471 (1980); SPIRES-HEP Oehme, R;
GAUGE FIELD PROPAGATOR AND THE NUMBER OF
R. Oehme and W. Zimmermann
Phys. Rev. D 21, 1661 (1980); SPIRES-HEP Oehme, R;
ON SUPERCONVERGENCE RELATIONS IN QUANTUM
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
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
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
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
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
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,
· (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.
R. Oehme Phys. Lett. B 195}, 60 (1987);
· RENORMALIZATION GROUP, BRST COHOMOLOGY, AND THE
PROBLEM OF CONFINEMENT
Phys. Rev. D 42, 4209 (1990);
· SUPERCONVERGENT GLUON PROPAGATOR AND THE
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
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
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
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