A Unified Algebraic Approach to Quantum Theory
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Conventional approaches to quantum mechanics are essentially dualistic. This is reflected in the fact that their mathematical formulation is based on two distinct mathematical structures: the algebra of dynamical variables (observables) and the vector space of state vectors. In contrast, coherent interpretations of quantum mechanics highlight the fact that quantum phenomena must be considered as undivided wholes. Here, we discuss a purely algebraic formulation of quantum mechanics. This formulation does not require the specification of a space of state vectors; rather, the required vector spaces can be identified as substructures in the algebra of dynamical variables (suitably extended for bosonic systems). This formulation of quantum mechanics captures the undivided wholeness characteristic of quantum phenomena, and provides insight into their characteristic nonseparability and nonlocality. The interpretation of the algebraic formulation in terms of quantum process is discussed.
- Barnes, B. A. (1980) Proc. Edinburgh Math. Soc. 23: pp. 229-238 CrossRef
- Bohm, D. J. (1957) Causality and Chance in Modern Physics. Routledge & Kegan Paul, London CrossRef
- Bohm, D. J. (1980) Wholeness and the Implicate Order. Routledge & Kegan Paul, London
- Bohm, D. J., Peat, F. D. (1988) Science, Order and Creativity. Routledge, London
- Dirac, P. A. M. (1958) The Principles of Quantum Mechanics. Oxford University Press, Oxford
- Dirac, P. A. M. (1965) Phys. Rev. 139: pp. 684-690 CrossRef
- Dirac, P. A. M. (1966) Lectures on Quantum Field Theory. Yeshiva University Belfer Graduate School of Science, New York
- Fernandes, M. (1995). “Geometric Algebras and the Foundations of Quantum Theory,” Ph.D. thesis, University of London.
- Fernandes, M., and Hiley, B. J. (1996). “The metaplectic group, the symplectic spinor and the Güoy phase,” submitted.
- Frescura, F. A. M., Hiley, B. J. (1980) Found. Phys. 10: pp. 7-31 CrossRef
- Frescura, F. A. M., Hiley, B. J. (1980) Found. Phys. 10: pp. 705-722 CrossRef
- Frescura, F. A. M., and Hiley, B. J. (1984). Rev. Brasil. Phys., vol. especial 70 anos de Mario Schönberg, 49–86.
- Guillemin, V., Sternberg, S. (1984) Symplectic Techniques in Physics. Cambridge University Press, Cambridge
- Hiley, B. J. (1980) Ann. Fond. Louis de Broglie 5: pp. 75-103
- Hiley, B. J., Fernandes, M. In: Ruhnau, E., Atmanspacher, H., Beiglboeck, W. eds. (1997) Time, Temporality and Now. Springer, Berlin
- Hiley, B., Monk, N. (1993) Mod. Phys. Lett. A 8: pp. 3625-3633 CrossRef
- Monk, N. A. M. (1994). “Algebraic Structures in the Light of the Implicate Order,” PhD thesis, University of London.
- Monk, N. A. M. (1997) Stud. Hist. Phil. Mod. Phys. 28: pp. 1-34 CrossRef
- von Neumann, J. (1931) Math. Ann. 104: pp. 570-578 CrossRef
- Weyl, H. (1950) The Theory of Groups and Quantum Mechanics. Dover, New York
- A Unified Algebraic Approach to Quantum Theory
Foundations of Physics Letters
Volume 11, Issue 4 , pp 371-377
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- quantum algebra
- quantum pre-space
- discrete Weyl algebra
- Clifford algebra
- implicate order