Prof. Dr. Gerd Rudolph - Publications
Books and Lecture Notes
Y.A. Kubyshin, J.M. Mourão, G. Rudolph, I.P. Volobuev:
Dimensional Reduction of Gauge Theories, Spontaneous Compactification and Model Building.
Lecture Notes in Physics 349. Springer 1989
Website
G. Rudolph, M. Schmidt:
Differential Geometry and Mathematical Physics Part I. Manifolds, Lie Groups and Hamiltonian Systems.
Springer 2012
Website
G. Rudolph, M. Schmidt:
Differential Geometry and Mathematical Physics Part II. Fibre Bundles, Topology and Gauge Fields.
Springer 2017
Website
Lecture Notes in German
I.P. Volobuev, G. Rudolph, M. Schmidt:
Komplexe halbeinfache Lie-Algebren und einige ihrer Anwendungen in Eichtheorien.
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G. Rudolph
Quantenmechanik 1.
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G. Rudolph
Quantenmechanik 2.
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Publications in Journals
F. Fürstenberg, G. Rudolph, M. Schmidt:
Defining relations for the orbit type strata of SU(2)-lattice gauge models.
To appear in J. Geom. Phys. 2017
arXiv:1702.01047
doi:10.1016/j.geomphys.2017.04.010
H. Grundling, G. Rudolph:
Dynamics for QCD on an infinite lattice.
Commun. Math. Phys. 349 (2017) 1163-1202
arXiv:1512.06319
doi:10.1007/s00220-016-2733-5
M. Hofmann, G. Rudolph, M. Schmidt:
On the reflection type decomposition of the adjoint reduced phase space of a compact semisimple Lie group.
J. Math. Phys. 54 (2013) 083505
arXiv:1302.6118
doi:10.1063/1.4817066
H. Grundling, G. Rudolph:
QCD on an infinite lattice.
Commun. Math. Phys. 318 (2013) 717-766
arXiv:1108.2129
doi:10.1007/s00220-013-1674-5
A. Hertsch, G. Rudolph and M. Schmidt:
Gauge orbit types for theories with gauge group O(n), SO(n) or Sp(n).
Ann. Inst. H. Poincaré 12 , No. 2 (2011) 351-395
doi:10.1007/s00023-011-0081-8
P.D. Jarvis, G. Rudolph and L.A. Yates:
A class of quadratic deformations of Lie superalgebras.
J. Phys. A: Math. Theor. 44 (2011) 235205
arXiv:1010.3765
doi:10.1088/1751-8113/44/23/235205
A. Hertsch, G. Rudolph, M. Schmidt:
Gauge orbit types for theories with classical compact gauge groups.
Rep. Math. Phys. 66 , No. 3 (2010) 331-353
arXiv:0812.0228
doi:10.1016/S0034-4877(11)00004-8
G. Rudolph, M. Schmidt:
On the algebra of quantum observables for a certain gauge model.
J. Math. Phys. 50 , 052102 (2009)
arXiv:0807.4646
doi:10.1063/1.3125184
J. Huebschmann, G. Rudolph, M. Schmidt:
A lattice gauge model for quantum mechanics on a stratified space.
Commun. Math. Phys. 286 (2009) 459-494
arXiv:hep-th/0702017
doi:10.1007/s00220-008-0693-0
S. Charzyński, G. Rudolph, M. Schmidt:
On the topology of the reduced classical configuration space of lattice QCD.
J. Geom. Phys. 58 (2008) 1607-1623
arXiv:hep-th/0512129
doi:10.1016/j.geomphys.2008.07.005
E. Fischer, G. Rudolph, M. Schmidt:
A lattice gauge model of singular Marsden-Weinstein reduction. Part I. Kinematics
J. Geom. Phys. 57 (2007) 1193-1213
arXiv:hep-th/0606132
doi:10.1016/j.geomphys.2006.09.008
Sz. Charzyński, J. Kijowski, G. Rudolph and M. Schmidt:
On the stratified classical configuration space of lattice QCD.
J. Geom. Phys. 55 (2005) 137-178
arXiv:hep-th/0409297
doi:10.1016/j.geomphys.2004.12.002
J. Kijowski and G. Rudolph:
The observable algebra of lattice QCD.
Rep. Math. Phys. 55 , No. 2 (2005) 199-210
doi:10.1016/S0034-4877(05)00013-3
P.D. Jarvis, J. Kijowski and G. Rudolph:
On the structure of the observable algebra of QCD on the lattice.
J. Phys. A: Math. Gen. 38 (2005) 5359-5377
arXiv:hep-th/0412143
doi:10.1088/0305-4470/38/23/020
J. Kijowski and G. Rudolph:
Charge superselection sectors for QCD on the lattice.
J. Math. Phys. 46 , 032303 (2005)
arXiv:hep-th/0404155
doi:10.1063/1.1851604
P. Jarvis and G. Rudolph:
Polynomial super-gl(n) algebras.
J. Phys. A, 36 , No. 20, (2003) 5531-5555
arXiv:hep-th/0301209
doi:10.1088/0305-4470/36/20/311
J. Kijowski, G. Rudolph and C. Śliwa:
Charge superselection sectors for scalar QED on the lattice.
Ann. Inst. H. Poincaré 4 (2003) 1137
arXiv:hep-th/0203214
doi:10.1007/s00023-003-0158-0
R. Matthes, O. Richter and G. Rudolph:
Spectral triples and differential calculi related to the Kronecker foliation.
J. Geom. Phys. 46 , (2003), 48-73
arXiv:math-ph/0201066
doi:10.1016/S0393-0440(02)00136-5
G. Rudolph, M. Schmidt:
On the orbit types of the action of the gauge group on connections modulo pointed gauge transformations.
Rep. Math. Phys. 50 (2002), 99-110
arXiv:math-ph/0104026
doi:10.1016/S0034-4877(02)80047-7
J. Kijowski, G. Rudolph:
On the Gauss law and global charge for QCD.
J. Math. Phys. 43 , No. 4 (2002) 1796-1808
arXiv:hep-th/0104052
doi:10.1063/1.1447310
G. Rudolph, M. Schmidt and I.P. Volobuev:
On the gauge orbit space stratification: a review.
J. Phys. A: Math. Gen. 35 (2002) R1-R50
arXiv:hep-th/0203027
doi:10.1088/0305-4470/35/28/201
G. Rudolph, M. Schmidt and I.P. Volobuev:
Partial ordering of gauge orbit types for SUn-gauge theories.
J. Geom. Phys. 42 (2002) 106-138
arXiv:math-ph/0009018
doi:10.1016/S0393-0440(01)00080-8
G. Rudolph, M. Schmidt and I.P. Volobuev:
Classification of gauge orbit types for SUn-gauge theories.
J. Math. Phys. Anal. Geom. 5 , (2002), 201-241
arXiv:math-ph/0003044
doi:10.1023/A:1020968206969
J. Kijowski, G. Rudolph, M. Rudolph:
Towards an effective field theory of QED.
Acta Phys. Polon. B 31 , n. 4 (2000) 847-861
arXiv:hep-th/9909113
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G. Rudolph, T. Tok, I.P. Volobuev:
Exact solutions in Einstein-Yang-Mills-Dirac systems.
J. Math. Phys. 40 , 11 (1999) 5890-5904
arXiv:gr-qc/9707060
doi:10.1063/1.533061
J. Kijowski, G. Rudolph, M. Rudolph:
Gauge invariant formulation and bosonization of the Schwinger model.
Phys. Lett. B 419 (1998) 285-290
arXiv:hep-th/9710003
doi:10.1016/S0370-2693(97)01486-X
J. Kijowski, G. Rudolph, C. Śliwa:
On the structure of the observable algebra for QED on the lattice.
Lett. Math. Phys. 43 (1998) 299-308
doi:10.1023/A:1007400816358
J. Kijowski, G. Rudolph, M. Rudolph:
Effective bosonic degrees of freedom for one-flavour chromodynamics.
Ann. Inst. H. Poincaré 68 , No. 3 (1998) 285-313
arXiv:hep-th/9606020
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J. Kijowski, G. Rudolph, M. Rudolph:
On the algebra of gauge invariants for one-flavour chromodynamics.
Rep. Math. Phys. 40 , No. 1 (1997) 131-142
doi:10.1016/S0034-4877(97)85624-8
J. Kijowski, G. Rudolph, A. Thielmann:
Algebra of observables and charge superselection sectors for QED on the lattice.
Commun. Math. Phys. 188 (1997) 535-564
doi:10.1007/s002200050178
G. Rudolph, T. Tok:
A certain class of Einstein-Yang-Mills systems.
Rep. Math. Phys. 39 , No. 3 (1997) 433-466
arXiv:gr-qc/9603017
doi:10.1016/S0034-4877(97)89758-3
G. Rudolph, T. Tok, I.P. Volobuev:
Exact solutions of the Reissner-Nordström type in Einstein-Yang- Mills systems with arbitrary gauge groups and space-time dimensions.
Int. J. Mod. Phys. A 11 , No. 28 (1996) 4999-5014
arXiv:gr-qc/9602006
doi:10.1142/S0217751X96002303
G. Rudolph, I.P. Volobuev:
Construction of grand unified models by dimensional reduction.
Int. J. Mod. Phys. A 11 , No. 12 (1996) 2127-2141
doi:10.1142/S0217751X96001073
R. Matthes, G. Rudolph, R. Wulkenhaar:
On the structure of a differential algebra used by Connes and Lott.
Rep. Math. Phys. 38 , No.1 (1996) 45-66
doi:10.1016/0034-4877(96)87677-4
R. Matthes, G. Rudolph, R. Wulkenhaar:
On a certain construction of graded Lie algebras with derivations.
J. Geom. Phys. 20 (1996) 107-141
doi:10.1016/0393-0440(95)00048-8
J. Kijowski, G. Rudolph, M. Rudolph:
Functional integral of QED in terms of gauge invariant quantities.
Lett. Math. Phys. 33 (1995) 139-146
doi:10.1007/BF00739802
A. Bohm, L.J. Boya, A. Mostafazadeh, G. Rudolph:
Classification theorem for principal fibre bundles, Berry's phase and exact cyclic evolution.
J. Geom. Phys. 12 (1993) 13-28
doi:10.1016/0393-0440(93)90085-S
J. Kijowski, G. Rudolph:
Spinor electrodynamics in terms of gauge invariant quantities.
Lett. Math. Phys. 29 (1993) 103-109
doi:10.1007/BF00749726
Yu.A. Kubyshin, O. Richter, G. Rudolph:
Invariant connections on homogeneous spaces.
J. Math. Phys. 34 (11) (1993) 5268-5282
doi:10.1063/1.530303
O. Richter, G. Rudolph:
Torsion and spontaneous compactification.
Int. J. Mod. Phys. A 8 , No.11 (1993) 1903-1921
doi:10.1142/S0217751X93000795
J. Dittmann, G. Rudolph:
On a connection governing parallel transport along 2x2-density matrices.
J. Geom. Phys. 10 (1992) 93-106
doi:10.1016/0393-0440(92)90008-O
J. Dittmann, G. Rudolph:
A class of connections governing parallel transport along density matrices.
J. Math. Phys. 33 (12) (1992) 4148-4154
doi:10.1063/1.529813
Yu.A. Kubyshin, O. Richter, G. Rudolph:
On the equations of spontaneous compactification for Gauss-Bonnet extended Einstein-Cartan theory.
Rep. Math. Phys. 30 , No. 3 (1992) 355-361
doi:10.1016/0034-4877(91)90064-T
G. Rudolph:
The functional integral on the lattice gauge orbit space.
Ann. d. Physik, 7.Folge, Band 47, Heft 2/3 (1990) 211-218
doi:10.1002/andp.19905020217
Yu. A. Kubyshin, G. Rudolph, I.M. Mourão, I.P. Volobuev:
Dimensional reduction of symmetric gauge fields, Higgs models and spontaneous compactification.
Fiz. Elem. Cast. i Atomn. Yadra 20 , 3 (1989) 561-627 (in Russian)
J. Kijowski, G. Rudolph:
The functional integral on the gauge orbit space for a non-Abelian Higgs model.
Nucl. Phys. B 325 (1989) 211-244
doi:10.1016/0550-3213(89)90379-9
G. Rudolph, I.P. Volobuev:
Some remarks on dimensional reduction of gauge theories and model building.
Nucl. Phys. B 313 (1989) 95-115
doi:10.1016/0550-3213(89)90515-4
G.Rudolph:
Gauge invariant quantities for a Higgs-model with gauge group SU(3).
Lett. Math. Phys. 16 (1988) 27-37
doi:10.1007/BF00398168
J. Kijowski, G. Rudolph:
A non-Abelian Higgs model on the lattice in terms of a complete system of gauge invariants.
Lett. Math. Phys. 15 (1988) 119-127
doi:10.1007/BF00397832
G. Rudolph:
Remarks on the problem of lifting space-time symmetries.
Lett. Math. Phys. 14 (1987) 133-138
doi:10.1007/BF00420303
G. Rudolph:
Classification of G-invariant configurations of Einstein-Cartan-theory on a multidimensional universe.
J. Geom. Phys. 4 , No. 1 (1987) 39-49
doi:10.1016/0393-0440(87)90010-6
J. Kijowski, G. Rudolph, A. Thielmann:
Symplectic structure of a non-Abelian Higgs model on the lattice.
Rep. Math. Phys. 24 , No. 3 (1986) 377-384
doi:10.1016/0034-4877(86)90011-X
G. Rudolph, I.P. Volobuev:
Geometrical approach to dimensional reduction of symmetric gauge fields.
Teor. Mat. Fiz. 62 , 3 (1985) 388-399; in English: 1985 Plenum Publ. Corp. 261-268
doi:10.1007/BF01018267
J. Kijowski, G. Rudolph:
New lattice approximation of gauge theories.
Phys. Rev. D 31 , No. 4 (1985) 856-864
doi:10.1103/PhysRevD.31.856
J. Kijowski, G. Rudolph:
On the hydrodynamical description of gauge theories.
J. Geom. Phys. 2 , No. 1 (1985) 25-33
doi:10.1016/0393-0440(85)90017-8
J. Kijowski, G. Rudolph:
Hydrodynamical description of theories of gauge fields interacting with matter fields.
Rep. Math. Phys. 21 , No. 3 (1985) 309-329
doi:10.1016/0034-4877(85)90035-7
J. Dittmann, G. Rudolph:
Canonical realizations of Lie algebras associated with foliated coadjoint orbits.
Ann. Inst. H. Poincaré 43 , No. 3 (1985) 251-267
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J. Kijowski, G. Rudolph:
Canonical structure of the theory of gauge fields interacting with matter fields.
Rep. Math. Phys. 20 , No. 3 (1984) 385-400
doi:10.1016/0034-4877(84)90046-6
J. Dittmann, G. Rudolph:
Konstruktion kanonischer Realisierungen der Lie-Algebra Sp(n,R) auf koadjungierten Orbits.
Wiss. Z. KMU 33 , Nr. 1 (1984) 4-13
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J. Kijowski, G. Rudolph:
Gitterapproximation der skalaren Elektrodynamik.
Wiss. Z. KMU 30 , Nr. 6 (1981) 613-621
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J. Kijowski, G. Rudolph:
On the Localization Problem in Relativistic Quantum Mechanics.
Bull. Acad. Pol. d. Sc., Vol. XXIV, No. 11 (1976) 1041-1048
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Contributions to conference proceedings
J. Huebschmann, G. Rudolph, M. Schmidt:
Quantum mechanical tunneling on a space with singularities.
Proc. of the VIIth International Workshop Lie Theory and Its Applications in Physics , Varna 2007, ed. H.-D. Doebner and V.K. Dobrev, Heron Press Science Series, Sofia 2008, pp. 190-210
G. Rudolph:
On the observable algebra and its representations for lattice QCD.
Proc. of the IVth International Symposium Quantum Theory and Symmetries IV , Varna 2005, Vol. 2, ed. V.K. Dobrev, Heron Press Science Series, Sofia 2006, pp. 429-441
J. Kijowski, G. Rudolph:
How to define coulor charge in quantum chromodynamics.
In Group 24: Physical and Mathematical Aspects of Symmetries, proc. of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris 2002, eds. J.-P. Gazeau et.al., Institute of Physics, Conference Series Number 173 (2003) 359-362
R. Matthes, O. Richter and G. Rudolph:
Generalized signature operators and spectral triples for the Kronecker foliation.
In: P.M. Hajac and W. Pusz (eds.), Noncommutative Geometry and Quantum Groups, Banach Center Publications 61 (2003) 125-147
J. Kijowski, G. Rudolph:
On the notion of global charge in QCD.
Rep. Math. Phys. 49 (2002) 211-224
G. Rudolph, M. Schmidt, I. P. Volobuev:
On the gauge orbit space stratification.
Proc. of the 2nd International Symposium Quantum Theory and Symmetries, Krakow 2001, eds. E. Kapuscik and A. Horzela, pp. 553-558
R. Matthes, O. Richter, G. Rudolph:
Spectral triples for the Kronecker foliation.
Proc. of the 2nd International Symposium Quantum Theory and Symmetries , Krakow 2001, eds. E. Kapuscik and A. Horzela, pp. 481-486
J. Kijowski, G. Rudolph:
Global Gauss law for lattice QCD.
Proc. of the 2nd International Symposium Quantum Theory and Symmetries , Krakow 2001, eds. E. Kapuscik and A. Horzela, pp. 96-105
G. Rudolph, M. Schmidt, I.P. Volobuev:
Some remarks on the gauge orbit space.
Proc. of the International Symposium on Quantum Theory and Symmetries, Goslar 1999, eds.: H.-D. Doebner et. al., World Scientific 2000, pp. 577-582
G. Rudolph, M. Schmidt, I.P. Volobuev:
Howe dual pairs and the structure of the gauge orbit space.
Proc. of the XIVth Workshop on High Energy Physics and Quantum Field Theory, Moscow 1999,
ed.: B.B. Levtchenko, Moscow University 2000, pp. 467-472
G. Rudolph, T. Tok, I.P. Volobuev:
Cosmological solutions with gauge and spinor fields.
Proc. of the XIIth Workshop on High Energy Physics and Quantum Field Theory, Samara 1997, ed.: B.B. Levtchenko, Moscow University 1999, pp. 376-388
J. Kijowski, G. Rudolph, M. Rudolph:
Gauge invariants and bosonization.
Proc. of the Conference Particles, Fields, and Gravitation , ed.: J. Rembielinski, AIP Conference Proceedings 453, Woodbury, Lodz 1998, pp. 382-393
G. Rudolph, T. Tok, I.P. Volobuev:
Reissner-Nordström solutions in Einstein-Yang-Mills systems.
Proceedings of the XIth Workshop on High Energy Physics and Quantum Field Theory, Sankt-Petersburg 1996,
ed.: B.B. Levtchenko, Moscow University 1997, pp. 361-367
J. Kijowski, G. Rudolph:
Algebra of observables for QED on a finite lattice.
Proc. of the 2nd International Workshop Lie Theory and its Applications in Physics II , eds.: H.-D. Doebner, V.K. Dobrev and J. Hilgert, World Scientific 1998, pp. 230-242
J. Kijowski, G. Rudolph:
Charge superselection sectors for QED on the lattice.
Proc. of the 5th Wigner Symposium, Wien 1997, eds.: P. Kasperkovitz, D. Grau, World Scientific 1998, pp. 216-218
J. Kijowski, G. Rudolph:
Lattice approximation of quantum electrodynamics.
In New Developments in Quantum Field Theory , Nato ASI Series B, Vol. 366, eds.: P.H. Damgaard, J. Jurkiewicz, Plenum Press 1998
G. Rudolph, T. Tok, I.P. Volobuev:
Exact solution of Reissner-Nordström type in Einstein-Yang-Mills theory.
Proc. of Group21, Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras,
Vol. 2, Goslar 1996, eds.: H.-D. Doebner, W. Scherer, J. Hilgert, World Scientific 1997, pp. 653-655
J. Kijowski, G. Rudolph, M. Rudolph:
Gauge theories with fermions in terms of gauge invariants.
Proc. of Group21, Physical Applications and Mathematical Aspects of Geometry, Groups and Algebras, Vol. 2, Goslar 1996, eds.: H.-D. Doebner, W. Scherer, J. Hilgert, World Scientific 1997, pp. 639-643
J. Kijowski, G. Rudolph, M. Rudolph:
Gauge theories in terms of invariants.
Proc. of the XXIXth Symposium on Mathematical Methods in Physics, Torun 1996,
Rep. Math. Phys. 40 , Nr. 3 (1997) 565-578
R. Matthes, G. Rudolph, R. Wulkenhaar:
Graded Lie algebras with derivation and model building.
Proc. of the Workshop Lie Theory and Its Physical Application , Clausthal 1995,
eds.: H.-D. Doebner, V.K. Dobrev, J. Hilgert, World Scientific 1996, pp. 149-158
R. Matthes, G. Rudolph, R. Wulkenhaar:
On certain graded Lie algebras arising in noncommutative geometry.
Acta Phys. Polon. B 27 , Nr. 10 (1996) 2755-2762,
Proc. of the 2nd German-Polish Symposium New Ideas in the Theory of Fundamental Interactions , Zakopane 1996
G. Rudolph, I.P. Volobuev:
Flipped SU(5)-grand unified model in the dimensional reduction method.
Proc. of the Zvenigorod Workshop, ed.: B.B. Levtchenko, Moscow University 1994, pp. 161-165
J. Kijowski, G. Rudolph:
Quantization of nonabelian gauge theories.
Proc. of the 1st Polish-German Meeting on Particles and Fields, Rydzyna 1992, ed.: H.D. Doebner, M. Pawlowski, R. Raczka, World Scientific 1994, pp. 73-82
O. Richter, G. Rudolph:
On Dimensional reduction of gravity with torsion.
Class. Quant. Grav. 10 (1993) S127-S134
J. Dittmann, G. Rudolph:
On a certain class of connections in the U(n)-bundle over density matrices.
Proc. of the II. Wigner-Symposium, Goslar 1991, ed.: H.D. Doebner, W. Scherer, F. Schroeck jr., World Scientific 1992,
J. Kijowski, G. Rudolph:
Quantization on the gauge orbit space.
Proc. of the II. Wigner-Symposium, Goslar 1991, ed.: H.D. Doebner, W. Scherer, F. Schroeck jr., World Scientific 1992, pp. 688-694
J. Kijowski, G. Rudolph:
Gauge invariant path integral and topological degrees of freedom for a non-Abelian Higgs model.
Proc. of XVII. Int. Conf. on Diff. Geom. Methods, Chester 1988, World Scientific 1990, pp. 116-129
G. Rudolph: Group-theoretical aspects of dimensional reduction.
Proc. of the XVI. Int.Coll. on Group-Theoretical Methods in Physics, Varna 1987, Lect. Notes in
Phys. 313 , pp. 485-497
G. Rudolph:
On dimensional reduction of Einstein-Cartan theory.
Proc. of Ahrenshoop-Coll. on High Energy Phys., 1986, pp. 215-225
G. Rudolph:
Construction of gauge invariant quantities for a non-Abelian Higgs-model on the lattice.
Proc. of the Conf. on High Energy Physics and Quantum Field Theory, Protvino 1986, pp. 98-109
G. Rudolph:
Lattice approximation of a non-Abelian Higgs model.
In Topics in Quantum Field Theory and Spectral Theory ,
Akad. d. Wiss. d. DDR, Berlin 1986, pp. 146-155
J. Dittmann, G. Rudolph:
Geometrical construction of canonical realizations of Lie-algebras.
Proc. of XIII. Int. Conf. in Theor. Phys., Shumen 1984, World Sci. Publ., pp. 25-37
G. Rudolph, I.P. Volobuev:
Dimensional reduction of gauge theories in terms of fibre bundle reduction.
Proc. of Int. Conf. on Diff. Geom. and Appl., Nove Mesto 1983, pp. 239-245
J. Dittmann, G. Rudolph:
Canonical realizations of Lie-algebras related to associated bundles.
Proc. of Int. Conf. on Diff. Geom. and Appl., Nove Mesto 1983, pp. 51-59