Abstract
In this paper we explore the mathematical foundations of quantum field theory. From the mathematical point of view, quantum field theory involves several revolutions in structure just as severe as, if not more than, the revolutionary change involved in the move from classical to quantum mechanics. Ordinary quantum mechanics is based upon real-valued observables which are not all compatible. We will see that the proper mathematical understanding of Fermi fields involves a new concept of probability theory, the graded probability space. This new concept also yields new points of view concerning ergodic theorems in statistical mechanics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Domb, C., and Green, M. (1972).Phase Transitions and Critical Phenomena, 6 Vols. Academic Press, New York.
Edwards, D. (1979). “The Mathematical Foundations of Quantum Mechanics,”Synthese 2, 1–70.
Edwards, D. (1981). “Phase Transitions and Critical Phenomena,” (Submitted).
Kadanoff, L. (1977). “The Application of Renormalization Group Techniques to Quarks and Strings,”Reviews of Modern Physics,49, No. 2.
Kostant, B. (1977). “Graded Manifolds, Graded Lie Theory, and Prequantization,” inDifferential Geometric Methods in Mathematical Physics, Vol. 570. Springer-Verlag, Heidelberg.
Ma, S. (1976).Modern Theory of Critical Phenomena. W. A. Benjamin, Inc., New York.
Osterwalder, K., and Seiler, E. (1981). “Gauge Field Theories on the Lattice,” (preprint).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Edwards, D.A. Mathematical foundations of quantum field theory: Fermions, gauge fields, and supersymmetry part I: Lattice field theories. Int J Theor Phys 20, 503–517 (1981). https://doi.org/10.1007/BF00669437
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00669437