Abstract
Microcausality is addressed for a class of Finslerian quantum fields in Minkowski spacetime by the calculation of the appropriate field commutators. It is demonstrated that, provided the adjoint field is consistently generalized, the necessary commutators are vanishing, and the field is microcausal. There are, however, Planck-scale modifications of the causal domain, but they only become significant for extremely large relative four-velocities at the separated spacetime points. For vanishing relative four-velocities, the causal domain is canonical.
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REFERENCES
H. E. Brandt, “Quantum fields in the spacetime tangent bundle,” Found. Phys. Lett. 11, 265-275 (1998).
H. E. Brandt, “Finslerian fields in the spacetime tangent bundle,” Chaos, Solitons & Fractals 10, 267-282 (1999).
H. E. Brandt, “Finslerian fields,” in Finslerian Geometries, P. L. Antonelli, ed. (Kluwer Academic, Dordrecht, 2000), pp. 131-138.
H. E. Brandt, “Particle geodesics and spectra in the spacetime tangent bundle,” Reports Math. Phys. 45, 389-405 (2000).
H. E. Brandt, “Finslerian spacetime,” Contemporary Math. 196, 273-287 (1996).
H. E. Brandt, “Structure of spacetime tangent bundle,” Found. Phys. Lett. 4, 523-536 (1991).
H. E. Brandt, “Maximal proper acceleration and the structure of spacetime,” Found. Phys. Lett. 2, 39-58, 405 (1989).
H. E. Brandt, “Riemann curvature scalar of spacetime tangent bundle,” Found. Phys. Lett. 5, 43-55 (1992).
H. E. Brandt, “Maximal proper acceleration relative to the vacuum,” Lett. Nuovo Cimento 38, 522-524 (1983); 39, 192 (1984).
S. Weinberg, The Quantum Theory of Fields, Volume I, Foundations (Cambridge University Press, Cambridge, 1995).
G. Kaiser, Quantum Physics, Relativity, and Complex Spacetime, Towards a New Synthesis (North-Holland, New York, 1990).
G. Kaiser, “Quantized fields in complex spacetime,” Ann. Phys. 173, 338-354 (1987).
E. Prugovecki, Stochastic Quantum Mechanics in Quantum Spacetime (Reidel, Dordrecht, 1986).
E. Prugovecki, Quantum Geometry: A Framework for Quantum General Relativity (Kluwer Academic, Dordrecht, 1992).
W. Greiner and J. Reinhardt, Field Quantization (Springer, Berlin, 1996).
R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That (Addison-Wesley, Redwood City, California, 1989).
K. Huang, Quantum Field Theory: From Operators to Path Integrals (Wiley-Interscience, New York, 1998).
L. S. Brown, Quantum Field Theory (Cambridge University Press, Cambridge, 1992).
D. I. Blokhintsev, Space and Time in the Microworld (Reidel, Dordrecht, 1973).
N. N. Bogolubov, A. A. Logunov, A. I. Oksak, and I. T. Todorov, General Principles of Quantum Field Theory (Kluwer Academic, Dordrecht, 1990).
S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson and Company, Evanston, Illinois, 1961).
N. N. Bogolubov, A. A. Logunov, and I. T. Todorov, Introduction to Axiomatic Quantum Field Theory (Benjamin, Reading, Massachusetts, 1975).
J. D. Bjorken, and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965).
W. Pauli, “The connection between spin and statistics,” Phys. Rev. 58, 716-722 (1940).
I. Duck and E.C.G. Sudarshan, Pauli and the Spin-Statistics Theorem (World Scientific, Singapore, 1997).
N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, third edn. (Wiley-Interscience, New York, 1980), pp. 603-606.
C. Møller, The Theory of Relativity, 2nd edn. (Clarendon, Oxford, 1972), p. 40.
A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms, Vol.1 (McGraw-Hill, New York, 1954), p. 75.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (National Bureau of Standards, Washington DC, 1972), p. 374.
E.C.G. Stückelberg, “La Mécanique du point matériel en théorie de relativité et en théorie des quanta,” Helv. Phys. Acta 15, 23-37 (1942).
R. P. Feynman, “A relativistic cut-off for classical electrodynamics,” Phys. Rev 74, 939-946 (1948).
R. P. Feynman, “The theory of positrons,” Phys. Rev. 76, 749-759 (1949).
G. Barton, Introduction to Advanced Field Theory (Wiley-Interscience, New York, 1963).
K. Gottfried and V. F. Weisskopf, Concepts of Particle Physics, Vol. II (Oxford University Press, Oxford, 1986), pp. 577-586.
T. Y. Cao, ed., Conceptual Foundations of Quantum Field Theory (Cambridge University Press, Cambridge, 1999), pp. 377-378.
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Brandt, H.E. FINSLERIAN QUANTUM FIELDS AND MICROCAUSALITY. Found Phys Lett 13, 307–328 (2000). https://doi.org/10.1023/A:1007871326346
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DOI: https://doi.org/10.1023/A:1007871326346