Covariant SPDEs and quantum field structures

Journal of Physics A: Mathematical and General

Volumn 31, Issue 1, 1998, Pages 231-258

  Becker, C ^a   Gielerak, R ^b   Lugiewicz P ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032498051     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/1/022     Document Type: Article

References (55)

1. Albeverio S and Hœgh-Krohn R 1986 Euclidean Markov fields and relativistic quantum fields from stochastic partial differential equations in four dimensions Phys. Lett. 177B 175-9
2. Albeverio S and Hœgh-Krohn R 1987 Quaternionic non-Abelian relativistic quantum fields in four space-time dimensions Phys. Lett. 189B 329-36
3. Albeverio S, Holden H, Hœgh-Krohn R and Kolsrud T 1989 Representation and construction of multiplicative noise J Funct. Anal. 87 250-72
4. Albeverio S, Iwata K and Kolsrud T 1990 Random fields as solutions of the inhomogeneous quaternionic Cauchy-Riemann equation. Invariance and analytic continuation Commun. Math. Phys. 132 555-80
5. Albeverio S, Iwata K and Schmidt M 1993 A convergent lattice approximation for nonlinear electromagnetic fields in four dimensions J. Math. Phys. 34 3327-42
6. Albeverio S and Wu J-L 1995 Euclidean random fields obtained by convolution from generalized white noise J. Math. Phys. 36 5217-45
7. Atiyah M F, Bott R and Shapiro A 1964 Clifford modules Topology 3 3-38
8. Becker C 1996 Reflection positively for quantum vector fields Stochastic Analysis and Applications, Proc. Fifth Gregynog Symp. ed I M Davies, A Truman and K D Elworthy (Singapore: World Scientific) pp 76-90
9. Becker C 1997 Euclidean quantum vector fields Preprint to appear
10. Berg C and Forst G 1975 Potential Theory on Locally Compact Abelian Groups (Berlin: Springer)
11. Boerner H 1970 Representations of Groups (Amsterdam: North-Holland)
12. Bogoliubov N N, Logunov A A, Oksak A I and Todorov I T 1990 General Principles of Quantum Field Theory (Dordrecht: Kluwer)
13. Booß-Bavnbek B and Wojciechowski K 1993 Elliptic Boundary Problems for Dirac Operators (Basel: Birkhäuser)
14. Broecker Th and tom Dieck T 1985 Representations of Compact Lie Groups (Berlin: Springer)
15. Fonda L and Ghirardi G C 1970 Symmetry Principles in Quantum Physics (New York: Marcel Dekker)
16. Fulton W and Harris J 1991 Representation Theory: A First Course (Berlin: Springer)
17. Gel'fand I M, Minlos R A and Shapiro Z Ya 1963 Representations of the Rotation and Lorentz Groups and their Applications (New York: Pergamon)
18. Gel'fand I M and Vilenkin N Ya 1964 Generalized Functions vol 4 (New York: Academic)
19. Gielerak R and Ługiewicz P 1997 4D-quantum field theories from covariant SPDE's Preprint JFT, University of Wroclaw
20. Gielerak R, Jakóbczyk L and Ługiewicz P 1997 Do there exist Euclidean random fields for spin s ≥ I bosonic quantum fields? Preprint to appear
21. Gilbert J E and Murray M 1991 Clifford Algebras and Dirac Operators in Harmonic Analysis (Cambridge: Cambridge University Press)
22. Ginibre J and Velo G 1975 The free Euclidean massive vector field in the Stückelberg gauge Ann. Inst. H. Poincaré A XXII 257-64
23. Gross L 1975 The free Euclidean proca and electromagnetic fields Functional Integration and its Applications. Proc. Int. Conf. (Cumberland Lodge, London, April 1974) ed A M Arthurs (Oxford: Clarendon) pp 69-82
24. Glimm J and Jaffe A 1987 Quantum Physics: A Functional Integral Point of View 2nd edn (Berlin: Springer)
25. Helgason S 1978 Differential Geometry, Lie Groups, and Symmetric Spaces (New York: Academic)
26. Ito K 1955 Isotropic random currents Proc. 3rd Berkeley Symp. on Mathematical Statistics and Probability vol II, pp 125-32
27. Iwata K 1990 On linear maps preserving Markov properties and applications to multicomponent generalized random fields Dissertation Ruhr-Universität Bochum
28. Jost R 1965 The General Theory of Quantized Fields: Lectures in Applied Mathematics (Providence. RI: American Mathematical Society)
29. Kerstan J, Matthes K and Mecke J 1978 Infinitely Divisible Stochastic Point Processes (London: Wiley)
30. Kusuoka S 1979 Markov fields and local operators J. Fac. Sci. Univ. Tokyo 26 199-212
31. Lawson H B Jr and Michelsohn M-L 1989 Spin Geometry (Princeton, NJ: Princeton University Press)
32. Ljubarski G J 1962 Anwendungen der Gruppentheorie in der Physik VEB Deutscher Verlag der Wissenschaften (Russian transl.)
33. Löffelholz J 1979 Proofs of Reflection Positivity for Transverse Fields (Colloquia Mathematica Soctetatis János Bolyai 27) Random Fields, Esztergom (Hungary)
34. Ługiewicz P 1997 Thesis Wrocław University, in preparation
35. Naimark M A 1958 Linieinyie Priedstavlienia Grupy Lorenca; Gosudarstwiennoie Izdatielsttwo Fiziko-Matiematicieskoi Literatury (Moscow) (Moscow: Isdatielstwo Nauka) (in Russian)
36. Nelson E 1973 The construction of quantum field theory from Markov fields J. Funct. Anal. 11 97-112
37. Nelson E 1973 The free Markov field J. Funct. Anal. 12 211-17
38. Osipov E P 1988 Octavic Markov cosurfaces and relativistic quantum fields in eight-dimensional space Preprint PPH No 19 Nowosybirsk
39. Osipov E P 1990 Two-dimensional random fields as solutions of stochastic differential equations Preprint (Bochum)
40. Osterwalder K and Schrader R 1973 Euclidean Fermi fields and a Feynman-Kac formula for boson-fermion models Helv. Phys. Acta 46 277-302
41. Osterwalder K and Schrader R 1973 Axioms for Euclidean Green's functions I Commun. Math. Phys. 31 83-112
42. Osterwalder K and Schrader R 1975 Axioms for Euclidean Green's functions II Commun. Math. Phys. 42 281-305
43. Ozkaynak H 1974 Euclidean fields for arbitrary spin particles Thesis Harvard University
44. 2 Euclidean (quantum) field theory (Princeton. NJ: Princeton University Press)
45. Streater R F and Wightman AS 1964 PCT Spin, Statistics and All That (New York: Benjamin)
46. Strocchi F 1978 Local and covariant gauge quantum field theories Phys. Rev. D 17 2010-21
47. Morchio G and Strocchi F 1980 Infrared singularities, vacuum structure and pure phases in local quantum-field theory Ann. Inst. H. Poincare A 33 251-82
48. Surgailis D 1979 On Covariant Stochastic Differential Equations and Markov Property of their Solutions (Instituto Fisica Universita di Roma)
49. Symanzik K 1969 Euclidean quantum field theory Local Quantum Theory ed R Jost (New York: Academic)
50. Velo G and Wightman A S (ed) 1978 Invariant wave equations Proc. Ettore Majorana Int. School Mathematical Physics, Erice (1977) ed G Velo and A S Wightman (Berlin: Springer)
51. Wong E and Zakai M 1989 Isotropic Gauss Markov currents Prob. Theor. Rel. Fields 82 137-54
52. Wong E and Zakai M 1989 Spectral representation of isotropic random currents Séminaire de Probabilites XXIII ed J Azéma, P Mayer and M Yor (Berlin: Springer)
53. Yao T H 1975 The connection between an Euclidean Gauss Markov vector field and the real proca Wightman field Commun. Math. Phys. 41 267-71
54. Yao T H 1976 Construction of quantum fields from Euclidean tensor fields J. Math. Phys. 17 241-7
55. Zelobenko D P 1970 Compact Lie Groups and their Representations (Moscow: Mir) (in Russian)