412
C Quantum Field Theory
Varying the gauge fixing fermion by δδ gives
Z =
dψ
r e
W [ψ r ]
∂ R S
∂ψ ∗
r
ψ ∗ =∂ ψ
∂(δδ)
∂ψ r .
(C.122)
Integrating by part gives the quantum master equation.
C.4
Suggested Readings
• Manipulations of functional integral are given in [11, sec. 15.1, 22.1, 17,
chap. 14, 7, 20].
• Zero-modes are discussed in [3].
• A general summary of path integrals for bosonic and fermionic fields can be
found in [21, app. A].
• BRST formalism: most QFT books contain an introduction; more complete
references are [27, chap. 15, 12, 26];
• BV formalism [27, chap. 15, 6, 9, 10, 12, 26] (several explicit examples are given
in [10, sec. 3], and see [1, 24, 29] for more specific details).
References
1. I.A. Batalin, G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators. Phys. Rev. D 28(10), 2567–2582 (1983). https://doi.org/10.1103/PhysRevD.28.2567
2. K. Becker, M. Becker, J.H. Schwarz, String Theory and M-Theory: A Modern Introduction, 1st
edn. (Cambridge University Press, Cambridge, 2006)
3. S.K. Blau, M. Visser, A. Wipf, Determinants, Dirac operators, and one-loop physics. Int. J.
Mod. Phys. A 4(6), 1467–1484 (1989) https://doi.org/10.1142/S0217751X89000625
4. R. Blumenhagen, D. Lüst, S. Theisen, Basic Concepts of String Theory. English. 2013 edn.
(Springer, Berlin, 2014)
5. R. Blumenhagen, E. Plauschinn, Introduction to Conformal Field Theory: With Applications
to String Theory. en. Lecture Notes in Physics (Springer, Berlin, 2009). https://www.springer.
com/de/book/9783642004490
6. B. DeWitt, The Global Approach to Quantum Field Theory. English. 1st edn. (Oxford
University Press, Oxford, 2014)
7. E. D’Hoker, D.H. Phong, The geometry of string perturbation theory. Rev. Mod. Phys. 60(4),
917–1065 (1988) https://doi.org/10.1103/RevModPhys.60.917
8. P. Di Francesco, P. Mathieu, D. Senechal, Conformal Field Theory, 2nd edn. (Springer, Berlin,
1999)
9. A. Fuster, M. Henneaux, A. Maas, BRST-antifield quantization: a short review. Int. J. Geom.
Methods Mod. Phys. 2, 939–964 (2005) https://doi.org/10.1142/S0219887805000892. arXiv:
hep-th/0506098
10. J. Gomis, J. Paris, S. Samuel, Antibracket, antifields and gauge-theory quantization. Phys.
Rep. 259(1–2), 1–145 (1995). https://doi.org/10.1016/0370-1573(94)00112-G. arXiv: hepth/9412228
11. B. Hatfield, Quantum Field Theory of Point Particles and Strings. English. (Addison Wesley,
Reading, 1998)
C Quantum Field Theory
Varying the gauge fixing fermion by δδ gives
Z =
dψ
r e
W [ψ r ]
∂ R S
∂ψ ∗
r
ψ ∗ =∂ ψ
∂(δδ)
∂ψ r .
(C.122)
Integrating by part gives the quantum master equation.
C.4
Suggested Readings
• Manipulations of functional integral are given in [11, sec. 15.1, 22.1, 17,
chap. 14, 7, 20].
• Zero-modes are discussed in [3].
• A general summary of path integrals for bosonic and fermionic fields can be
found in [21, app. A].
• BRST formalism: most QFT books contain an introduction; more complete
references are [27, chap. 15, 12, 26];
• BV formalism [27, chap. 15, 6, 9, 10, 12, 26] (several explicit examples are given
in [10, sec. 3], and see [1, 24, 29] for more specific details).
References
1. I.A. Batalin, G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators. Phys. Rev. D 28(10), 2567–2582 (1983). https://doi.org/10.1103/PhysRevD.28.2567
2. K. Becker, M. Becker, J.H. Schwarz, String Theory and M-Theory: A Modern Introduction, 1st
edn. (Cambridge University Press, Cambridge, 2006)
3. S.K. Blau, M. Visser, A. Wipf, Determinants, Dirac operators, and one-loop physics. Int. J.
Mod. Phys. A 4(6), 1467–1484 (1989) https://doi.org/10.1142/S0217751X89000625
4. R. Blumenhagen, D. Lüst, S. Theisen, Basic Concepts of String Theory. English. 2013 edn.
(Springer, Berlin, 2014)
5. R. Blumenhagen, E. Plauschinn, Introduction to Conformal Field Theory: With Applications
to String Theory. en. Lecture Notes in Physics (Springer, Berlin, 2009). https://www.springer.
com/de/book/9783642004490
6. B. DeWitt, The Global Approach to Quantum Field Theory. English. 1st edn. (Oxford
University Press, Oxford, 2014)
7. E. D’Hoker, D.H. Phong, The geometry of string perturbation theory. Rev. Mod. Phys. 60(4),
917–1065 (1988) https://doi.org/10.1103/RevModPhys.60.917
8. P. Di Francesco, P. Mathieu, D. Senechal, Conformal Field Theory, 2nd edn. (Springer, Berlin,
1999)
9. A. Fuster, M. Henneaux, A. Maas, BRST-antifield quantization: a short review. Int. J. Geom.
Methods Mod. Phys. 2, 939–964 (2005) https://doi.org/10.1142/S0219887805000892. arXiv:
hep-th/0506098
10. J. Gomis, J. Paris, S. Samuel, Antibracket, antifields and gauge-theory quantization. Phys.
Rep. 259(1–2), 1–145 (1995). https://doi.org/10.1016/0370-1573(94)00112-G. arXiv: hepth/9412228
11. B. Hatfield, Quantum Field Theory of Point Particles and Strings. English. (Addison Wesley,
Reading, 1998)