An introduction to quantum field theory
1995
Abstract
Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in Euclidean space, where there is an immediate connection with the rules for Feynman diagrams and the partition function of Statistical Mechanics.
References (69)
- W. Pauli, "Die allgemeinen Prinzipien der Wellenmechanik", Handbuch der Physik Vol. XXIV/1, ed. H. Geiger and K. Scheel (Springer, Berlin 1933) pp. 83-272, reprinted in Handbuch der Physik -Encyclopaedia of Physics Vol.
- V/1, ed. S. Flugge (Springer, Berlin 1958) pp. 1-168, and as a separate volume, ed. N. Straumann (Springer, Berlin and Heidelberg 1990). English version: "General Principles of Quantum Mechanics", trans. P. Achutan and K. Venkatesan (Springer, Berlin and Heidelberg 1980).
- A. Einstein, Phys. Z. 18 (1917) 121;
- R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectures in Physics (Addison-Wesley, 1965), Vol. I, sect. 42-5 and Vol. III, sect. 4-4.
- P. A. M. Dirac, Proc. Roy. Soc. A 114 (1927) 243.
- J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York 1965).
- T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood, Chur 1981).
- L. H. Ryder, Quantum Field Theory (Cambridge University Press, Cambridge 1985).
- N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (John Wiley, New York 1980).
- S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper & Row, New York 1961).
- C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York 1980).
- F. Mandl and G. Shaw, Quantum Field Theory, revised ed. (John Wiley, Chichester 1993).
- S. N. Gupta, Proc. Phys. Soc. (London) A 63 (1950) 681; K. Bleuler, Helv. Phys. Acta 23 (1950) 567.
- G. Baym, Lectures on Quantum Mechanics (Benjamin/Cummings, Reading Ma. 1969).
- J. J. Sakurai, Modern Quantum Mechanics (Benjamin/Cummings, Menlo Park Ca. 1985).
- D. M. Brink and G. R. Satchler, Angular Momentum, 3rd ed. (Oxford Uni- versity Press, Oxford 1968).
- M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York 1957);
- A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton NJ 1957).
- A. S. Wightman, in The Lesson of Quantum Theory, ed. J. de Boer, E. Dal, and O. Ulfbeck (North-Holland, Amsterdam 1986).
- J. R. Klauder and B.-S. Skagerstam, Coherent States: Applications in Physics and Mathematical Physics (World Scientific, Singapore 1985).
- P. Jordan and W. Pauli, Z. Phys. 47 (1928) 151.
- N. Bohr and L. Rosenfeld, Det. Kgl. Dan. Vid. Selsk., Mat.-fys. Medd. 12 (1933) no. 8, and Phys. Rev. 78 (1950) 794, translated/reprinted in Selected Pa- pers of Léon Rosenfeld , ed. R. S. Cohen and J. Stachel (Reidel, Dordrecht 1979) pp. 357-412, and in Quantum Theory and Measurement, ed. J. A. Wheeler and W. H. Zurek (Princeton Univ. Press, Princeton NJ 1983) pp. 477-534.
- R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That (Benjamin, New York 1964)
- R. Jost, The General Theory of Quantized Fields (Am. Math. Soc., Providence R.I. 1965).
- R. Haag, Local Quantum Physics (Springer-Verlag, Berlin 1992).
- W. Heitler, The Quantum Theory of Radiation, 3rd ed. (Oxford University Press, Oxford 1954);
- E. Corinaldesi, Suppl. Nuovo Cimento (Series IX) 10 (1953) 83; L. Rosenfeld, in Niels Bohr and the Development of Physics, ed. W. Pauli (Pergamon Press, London 1955) p. 70; K. Gottfried, Quantum Mechanics (Benjamin/Cummings, Reading Ma. 1966).
- M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory, Vols. 1 and 2 (Cambridge Univ. Press, Cambridge 1987).
- M. Fierz, Helv. Phys. Acta 12 (1939) 3.
- W. Pauli, Phys. Rev. 58 (1940) 716.
- G. Lüders and B. Zumino, Phys. Rev. 110 (1958) 1450;
- N. Burgoyne, Nuovo Cimento 8 (1958) 807.
- W. Pauli, in Niels Bohr and the Development of Physics, ed. W. Pauli (Perg- amon Press, London 1955) p. 30.
- J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York 1964).
- P. Jordan and E. Wigner, Z. Phys. 47 (1928) 631.
- W. Heisenberg and W. Pauli, Z. Phys. 56 (1929) 1; 59 (1930) 168;
- W. Pauli, Collected Scientific Papers, Vol. 2, ed. R. Kronig and V. F. Weisskopf (Wiley, New York 1964).
- R. P. Feynman, Rev. Mod. Phys. 20 (1948) 267; Phys. Rev. 80 (1950) 440;
- R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York 1965).
- Particle Data Group: L. Montanet et al., Phys. Rev. D 50 (1994) 1173.
- P. A. M. Dirac, Can. J. Math. 2 (1950) 120; Proc. Roy. Soc. 246 (1958) 326: Lectures on Quantum Mechanics (Belfer Graduate School, Yeshiva Univ. 1964).
- K. G. Wilson, Phys. Rev. 179 (1969) 1499.
- J. Schwinger (ed.), Selected Papers on Quantum Electrodynamics (Dover, 1958).
- J. C. Collins, Renormalization: an Introduction to Renormalization, the Renormalization Group, and the Operator-Product Expansion (Cambridge Univ. Press, Cambridge 1984).
- K. Symanzik, Nucl. Phys. B 190 (1981) 1; Structural Elements in Particle Physics and Statistical Mechanics, Proc. NATO Adv. Summer Inst. in Theo- retical Physics, Freiburg 1981, ed. J. Honerkamp, K. Pohlmeyer and H. Römer (Plenum, New York 1983) p. 287.
- S. L. Adler, Phys. Rev. 177 (1969) 2426; J. S. Bell and R. Jackiw, Nuovo Cimento 60 A (1969) 47; S. L. Adler, Lectures on Elementary Particles and Quantum Field Theory, Vol. 1, eds. S. Deser, M. Grisaru and H. Pendleton (MIT Press, Cambridge MA 1970).
- H. Fritzsch and M. Gell-Mann, Proc. XVI Int. Conf. on High Energy Physics, Chicago 1972, Vol. 2, ed. J. D. Jackson and A. Roberts (National Accelerator Laboratory, Batavia IL 1972);
- S. Weinberg, Phys. Rev. Letters 31 (1973) 494;
- Phys. Rev. D 8 (1973) 4482; H. Fritzsch, M. Gell-Mann and H. Leutwyler, Phys. Letters 47 (1973) 365.
- F. J. Ynduráin, Quantum Chromodynamics -An Introduction to the Theory of Quarks and Gluons, 1st ed. (Springer-Verlag, New York 1983); The The- ory of Quark and Gluon Interactions, 2nd ed. (Springer-Verlag, Berlin and Heidelberg 1993).
- A. S. Wightman, Phys. Rev. 101 (1956) 860.
- F. J. Dyson, Phys. Rev. 75 (1949) 1736; G. C. Wick, Phys. Rev. 96 (1954) 1124; S. Weinberg, Phys. Rev. 118 (1960) 838.
- J. Schwinger, Proc. Nat. Acad. Sci. 44 (1958) 956.
- K. Symanzik, in Analysis in Function Space, ed. W. T. Martin and I. Segal (MIT Press, Cambridge MA 1964) p. 197; J. Math. Phys. 7 (1966) 510, and in Local Quantum Field Theory, ed. R. Jost (Academic Press, New York 1969) p. 152.
- B. Simon, The P (φ) 2 Euclidean (Quantum) Field Theory (Princeton Univ. Press, Princeton NJ 1974).
- P. A. M. Dirac, Phys. Z. der Sowjetunion 3 (1933) 64.
- F. A. Berezin, The Method of Second Quantization (Academic Press, New York 1966).
- J. C. Taylor, Gauge Theories of Weak Interactions (Cambridge Univ. Press, Cambridge 1978).
- P. Ramond, Field Theory, a Modern Primer (Benjamin/Cummings, Reading MA 1981).
- L. D. Fadde'ev and A. A. Slavnov, Gauge Fields (Benjamin/Cummings, New York 1980).
- R. J. Rivers, Path Integral Methods in Quantum Field Theory (Cambridge Univ. Press, Cambridge 1987).
- J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford Univ. Press, Oxford 1993).
- J. Schwinger, Phys. Rev. 82 (1951) 914; Proc. Nat. Acad. Sci. 37 (1951) 452; Phys. Rev. 91 (1953) 713.
- K. G. Wilson Phys. Rev. D 10 (1974) 2445;
- M. Creutz, Quarks, Gluons and Lattices (Cambridge Univ. Press, Cambridge 1983);
- H. J. Rothe, Lattice Gauge Theories (World Scientific, Singapore 1992).
- J. L. Gervais and B. Sakita, Phys. Rev. D 11 (1975) 2943;
- A. Jevicki, Nucl. Phys. B 117 (1976) 365; G. 't Hooft, Phys. Rev. D 14 (1976) 3432.
- S. W. Hawking, Comm. Math. Phys. 55 (1977) 133.