Gerhard Mack


H. A. Kastrup, G. Mack, A method for determining the electromagnetic form factors of nucleons by cosmic ray experiments, Phys. Letters 22 (1966) 331

G. Mack, High momentum transfer behavior of the electromagnetic form factor of the nucleon, Phys. Rev. 154 (1967) 1617

G. Mack, Partially conserved dilatation current, Dissertation Bern 1967, short extract Nucl. Phys. B5 (1968) 499

G. Mack, A meson bremsstrahlung model taking phase space into account, Phys. Letters 26B (1968) 515

G. Mack, Abdus Salam, Finite component field representations of the conformal group, Ann. Phys. (N.Y.) 53 (1969) 174

G. Mack, I.Todorov, Irreducibility of the ladder representations of U (2, 2) when restricted to the Poncar´e subgroup, J. Math. Phys. 10 (1969) 2078

G.J. Iverson, G. Mack, Theory of weak interactions with “continuous spin” neutrinos, Phys. Rev. D2 (1970) 2326

G.J. Iverson, G. Mack, E2-parametrization of SL (2, C), J. Math. Phys. 11 (1970) 1581

G.J. Iverson, G. Mack, Quantum fields and interactions of massless particles: the continuous spin case, Ann. Phys. (N.Y.) 64 (1971) 211

G. Mack, Universality of deep inelastic lepton hadron scattering, Phys. Rev. Letters 25 (1970) 400

G. Mack, The scaling law of electroproduction as a consequence of broken dilatation symmetry, Nucl. Phys. B35 (1971) 592

G. Mack, Fixed poles and light cone singularities, Phys. Letters 35B (1971) 234

13. G. Mack, Does the brain have symmetry? I. Vision, report CTS-B-71-2 (Center for Theoretical Studies, Coral Gables) 1971
G. Mack, I. Todorov, Conformal invariant Green functions without ultraviolet divergences, Phys. Rev. D8 (1971) 1764

G. Mack, K. Symanzik, Currents, stress energy tensor and generalized unitarity in conformal invariant quantum field theory, Commun. Math. Phys. 27 (1972) 247

G. Mack, Expansions around canonical dimensions in conformal invariant quantum field theory, Bern preprint April 1972 (unpublished)

G. Mack, Conformal invariance and short distance expansions in quantum field theory, Lecture Notes in Physics 17 (1973) 300, Springer Verlag Heidelberg

G. Mack, Group theoretical approach to conformal invariant quantum field theory, J. de physique 34 C1 (Suppl. No. 10) (1973) 99 and in Renormalization and invariance in quantum field theory, E.R. Caianello (ed) Plenum Press New York 1974

G. Mack, Osterwalder Schrader positivity in conformal invariant quantum field theory, Lecture Notes in Physics 37 (1975) 66

M. Lüscher, G. Mack, Global conformal invariance, Commun. Math. Phys. 41 (1975) 203


G. Mack, On Blattners formula for the discrete series representations of SO(2n, 1), J. Functional Analysis 23 (1976) 311

G. Mack, Conformal invariant quantum field theory in: New developments in quantum field theory and statistical mechanics (NATO ASI, Carg`ese 1976) Plenum Press New York 1976

G. Mack, Duality in quantum field theory, Nucl. Phys. B118 (1977) 445

G. Mack, Convergence of operator pproduct expansions on the vacuum in conformal invariant quantum field theory, Commun. Math. Phys. 53 (1977) 155

V.K. Dobrev, G. Mack, V.B. Petkova, S.G. Petrova, I.T. Todorov, Harmonic analysis on the n-dimensional Lorentz group and its application to conformal quantum field theory, Lecture Notes in Physics 63, Springer Verlag Heidelberg 1977


V.K. Dobrev, G. Mack, V.B. Petkova, S.G. Petrova, I.T. Todorov, On Clebsch Gordan expansions for the Lorentz group in n dimensions, Reports on Math. Phys. 9 (1976) 219

G. Mack, All unitary ray representations of the conformal group SU(2,2) with positive energy, Commun. Math. Phys. 55 (1977) 1

28. M. Lüscher, G. Mack, The energy momentum tensor of critical field theories in 1+1 dimensions, 1977 (unpublished manuscript)

G. Mack, Quark and color confinement through dynamical Higgs mechanism, DESY 77/58, Aug. 1977

G. Mack, Colour screening and quark confinement, Phys. Letters 79B (1978) 263

G. Mack, V.B. Petkova, Comparison of lattice gauge theory with gauge group Z2 and SU (2), Ann. Phys. (N.Y.) 123 (1978) 442

G. Mack, V.B. Petkova, Sufficient condition for confinement of static quarks by a vortex condensation mechanism, Ann. Phys. (N.Y.) 125 (1979) 117

G. Mack, V.B. Petkova, Z2 -monopoles in the standard SU (2)-lattice gauge theory model, DESY 79/22 (Apr. 79) and Z. Physik C12 (1982) 177

G. Mack, Lattice field theory, in: Lecture Notes in Physics 153 (1982) Springer Verlag Heidelberg

G. Mack, Confinement of static quarks in 2-dimensional lattice gauge theories, Commun. Math. Phys. 65 (1979) 91

G. Mack, Properties of lattice gauge theory models at low temperatures, in: Recent developments in gauge theories (NATO ASI Carg`ese 1979), G. ’t Hooft et al (eds), Plenum Press New York 1980

G. Mack, Predictions of a theory of quark confinement, Phys. Rev. Letters 45 (1980) 1378

G. Mack, Quark confinement in lattice gauge theory, Acta Physica Austriaca, Suppl. XXII (1980) 509

G. Mack, E. Pietarinen, Test of some current ideas in quark confinement physics by Monte Carlo simulations for finite lattices, Phys. Letters 94B(1980) 397

G. Mack, Physical principles, geometrical aspects and locality of gauge field theories, Fortschritte der Physik 81 (1981) 135

M. Göpfert, G. Mack, Iterated Mayer expansions for classical gases at low temperatures, Commun. Math. Phys. 81 (1981) 97


M. Göpfert, G. Mack, Proof of confinement in 3-dimensional U (1) lattice gauge theory for all values of the coupling constant, Commun. Math. Phys. 82 (1982) 545


G. Mack, H. Meyer, A disorder parameter that tests for confinement in gauge theories with quark fields, Nucl. Phys. B200[FS4] (1982) 249

G. Mack, E. Pietarinen, Monopoles, vortices and confinement, Nucl. Phys. B205[FS5] (1982) 141


M. Göpfert, G. Mack, Renormalization group aspects of 3-dimensional pure U (1) lattice gauge theory, in: Structural elements in particle physics and statistical mechanics, J. Honerkamp et al (eds.), Plenum Press New York 1983


M. Karliner, G. Mack, Mass gap and string tension in QED3 : Comparison of theory and Monte Carlo simulations, Nucl. Phys. 225[FS9] (1983) 371


G. Mack, Nonperturbative methods, Lecture Notes in Physics 181 (1983) 35

G. Mack, Renormalization group and Mayer expansions, in: Progress in gauge field theory (NATO ASI Carg`ese 1983), G. ’t Hooft et al (eds), Plenum Press New York 1983

G. Mack, Dielectric lattice gauge theory, Nucl. Phys. B235[FS11] (1984) 197

G. Mack, A. Pordt, Convergent perturbation expansions for Euclidean quantum field theories, Commun. Math. Phys. 97 (1985) 267

G. Mack, K. Pinn, Restrictions of effective dielectric lattice gauge theory actions from their analytic properties, DESY 86-127 (1986)

G. Mack, K. Pinn, A Monte Carlo procedure for Hamiltonians with small nonlocal correction terms, Phys. Letters 137 (1986) 434

G. Mack, Introduction to conformal invariant quantum field theories in two and more dimensions, in: Nonperturbative quantum field theory, (NATO ASI Carg`ese 1987) G. ’t Hooft et al (eds), Plenum Press New York 1988

G. Mack, Multigrid methods in quantum field theory in: Nonperturbative quantum field theory G. ’t Hooft et al (eds) Plenum Press New York 1988

D. Buchholz, G. Mack, I. Todorov, The current algebra on the circle as a germ of local field theories Nucl. Phys. (Proc. Suppl) 5B (1988) 20-56

G. Mack, A. Pordt, Convergent weak coupling expansions for lattice field theories that look like perturbation series Rev. Math. Physics 1 (1989) 47-87

G. Mack, S. Meyer, The effective action from multigrid Monte Carlo Nucl. Phys. (Proc. Suppl.) 17 (1990) 293

G. Mack, V. Schomerus, Endomorphisms and quantum symmetry of the conformal Ising model in: Algebraic theory of superselection sectors, D. Kastler (ed) World Scientific Singapore 1990

G. Mack, V. Schomerus, Conformal field algebras with quantum symmetry from the theory of superselection sectors Commun. Math. Phys. 134 (1990) 139

D. Buchholz, G. Mack, R. Paunov, I. Todorov, An algebraic approach to the classification of local conformal field theories, Proc. Math. Physics Conference, Swansea 1988

M. Hasenbusch, S. Meyer und G. Mack, Noncritical multigrid Monte Carlo: O(3) nonlinear a-model, Nucl.Phys.B (Proc.Suppl.) 20 (1991),110

G. Mack, V. Schomerus, Quasi Hopf quantum symmetry in quantum theory Nucl. Phys 370 (1992) 185

G. Mack, V. Schomerus, Quasi quantum group symmetry and local braid relations in the conformal Ising model Phys. Letters 267 (1991) 207

T. Kalkreuter, G. Mack, M. Speh, Blockspin and multigrid for staggered fermions in Non-Abelian gauge fields in Fermion algorithms H.J. Herrmann and F. Karsch (eds) World Scientific 1991

G. Mack, V. Schomerus Quantum symmetry in quantum theory in: New symmetry principles in quantum field theory J. Fröhlich et al (eds) Plenum Press 1991


G. Mack, V. Schomerus Action of truncated quantum groups on quasi quantum planes and a quasi associative differential geometry and calculus Commun. Math. Phys. 149 (1992) 513


G. Mack, V. Schomerus Quantensymmetrie in der Quantentheorie Phys. Blätter 49 (1993) 883 


G. Mack, V. Schomerus, Quantum symmetry for pedestrians DESY-9253 (Nov. 1992)

D. Buchholz, G. Mack, I. Todorov, Localized automorphisms of the current algebra on the circle: An instructive example in: Algebraic theory of superselection sectors D. Kastler (ed) World Scientific Singapore 1990

T. Kalkreuter, G. Mack, G. Palma, M. Speh, Effective field theories in: Lecture Notes in Physics 409 Springer Verlag 1992

G. Mack, Conformal symmetry and quantum space time, Salamfest proceedings, World Scientific Singapore 1994

G. Mack, V. Schomerus, Models of quantum space time: quantum field planes, Proc. Caribbean school, Guadeloupe June 1993

G. Mack, V. Schomerus, A short introduction to quantum symmetrty J. Geom. Phys. 11 (1993) 361


M. Bäker, T. Kalkreuter, G. Mack, M. Speh, Neural multigrid for gauge theories and other disordered systems, Int. J. Mod. Phys. C4 (1993) 239


M. Bäker, G. Mack, M. Speh, Neural Multigrid for Disordered Systems: Lattice Gauge Theory as Example in: Handbook of Neural Computation, IOP Publishing Ltd and Oxford University Press, 1996


M. Bäker, G. Mack, and M. Speh, Multigrid meets neural nets, Nucl. Phys. B (Proc. Suppl.)30 (1993) 269


G. Mack, Universal dynamics of complex adaptive systems: Gauge theory of things alive DESY-94-075 (Apr 94)

G. Mack, Gauge theory of things alive and universal dynamics DESY 94-184 (Oct. 94), short version in Nucl. Phys. (Proc. Suppl.) B42 (1995) 923

U. Kerres, G. Mack, G. Palma, A selfconsistent study of of the phase transition in the scalar elektroweak theory at finite temperature Nucl. Phys. (Proc. Suppl.) 42 (1995) 584

U. Kerres, G. Mack, G. Palma, Perfect 3-dimensional lattice actions for 4-dimensional quantum field theories at finite temperatures, Nucl. Phys. B467 (1996) 510

M. Griessl, G. Mack, G. Palma, Y. Xylander, Self-consistent Calculation of Real Space Renormalization Group Flows and Effective Potentials, Nucl. Phys. B477 (1996) 878


G. Mack, Theorie des Lebendigen in: Komplexe Adaptive Systeme (S. Bornholdt, P. Feindt, eds) R¨oll Verlag 1996


G. Mack, Gauge Theory of things alive: Universal Dynamics as a tool in Parallel Computing, Suppl. Progr. Theor. Physics (Kyoto) 122 (1996) 201

G. Mack, Pushing Einsteins principles to the extreme in: G t’Hooft et al (eds), Quantum Fields and Quantum Space Time, NATO ASI vol B364 Plenum Press, New York 1997

G. Mack, Emergent behavior: a case of order vs. disorder, (1998), unpublished

G. Mack, To gauge theory from a minimum of a priori structure, Proc. Steklov Math. Institute 226 (1999) 208-216

M. Meier-Schellersheim, G. Mack, SIMMUNE, a tool for simulating and analyzing Immune System behavior, DESY 99-034, March 1999, submitted for publication to Bull. Math. Biology e-print arXiv: cs.MA/9903017

G. Mack, J. Würthner, Life in Silico -Simulations of Complex Systems by Enzymatic Computation, DESY report 00-147, Oct 2000, e-print arXiv: physics/0011020

M. Bartels, G. Mack, G. Palma, Analytic calculation of the 1-loop effective action for the O(N + 1)-symmetric 2-dimensional nonlinear amodel, Nucl. Phys. B612 [FS] (2001) 413-445

G. Mack, Universal dynamics, a Unified Theory of Complex Systems. Emergence, Life and Death, Commun. Math. Phys. 219 (2001) 141-178, e-print arXiv: hep-th/0011074

C. Lehmann, G. Mack, T. Prüstel, Origin of quark masses and Kobayashi Maskawa matrix in a gauge theory with nonunitary parallel transporters, e-print arXiv: hep-ph/0305331, 2003


G. Mack, M. de Riese, Simple space time symmetries: Generalizing conformal field theory, J. Math. Phys. 48, 052304 (2007)(21 pages), e-print arXiv: hep-th/0410277 (2004)

C. Lehmann, G. Mack, Gauge theories with nonunitary parallel transporters: A soluble Higgs model, Eur.Phys.J. C39 483-497 (2005)

G. Mack, G. Palma, L. Vergara, Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-Model, Phys. Rev. E (in press) arXiv: cond-mat/0506713 (2005)

G. Mack, T. Prüstel, Generalized gauge theories with nonunitary parallel transport: General relativity with cosmological constant as an example, Eur.Phys.J. C46 255-267 (2006)


G. Mack, J. Würthner, System Class Laboratory , a software package for modelling and simulating complex systems. Not yet released


G. Mack, D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models, arXiv:0907:2407 (2009)

G. Mack, D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models, arXiv:0909.1024 (2009) to appear in Bulg. J. Physics

G. Mack, Was die Welt im Innersten zusammenhält, erscheint im Programmheft der Faust I/II Inszenierung Thalia Theater Hamburg (2011)



G. Mack, S. Wallentowitz, P. E. Toschek, Decoherence in Generalized Measurement and the Quantum Zeno Paradox, Physics Reports 540 (2014) 1-23

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