Abstract
\(\phi^{4}\)\(\overline{{MS}})\) Effective field theories are among the most powerful instruments in the toolbox of contemporary physics. Although the concept of effective field theory has been already discussed in Chap. 8, here we are going to provide a relatively elementary description of the relevant technology. Although rather unrealistic, the examples of effective field theories studied next serve the purpose of illustrating the relevant physics involved. The chapter will be closed with a discussion of the concept of naturalness, which plays a central role in modern particle physics. The reader is advised not to be scared by the technicalities of the Feynman diagram computations contained in the chapter. Most of the conclusions can be reached without caring too much about the precise value of the numerical prefactors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Our choice of natural units allows us to specify the dimensions of all quantities in terms of powers of energy. Thus, for the coordinates we have \([x^{\mu}]=E^{-1}\), which we denote by \(D_{x}=-1\).
- 2.
The other known way of canceling quadratic divergences is to have supersymmetry (see Sect. 13.2 ), where the quadratically divergent corrections to the scalar masses are cancelled by the contribution of diagrams with fermion loops.
- 3.
As a matter of fact, once we decide that lepton number conservation is not a fundamental symmetry we can also introduce, in addition to the Dirac masses, Majorana mass terms for the right-handed neutrinos.
References
’t Hooft, G., Veltman, M.J.G.: Regularization and renormalization of gauge fields. Nucl. Phys. B 44, 189 (1972)
Bollini, C.G., Giambiagi, J.J.: Dimensional renormalization: the number of dimensions as a regularizing parameter. Nuovo Cim. B 12, 20 (1972)
’t Hooft, G.: Dimensional regularization and the renormalization group. Nucl. Phys. B 61, 455 (1973)
’t Hooft, G.: The renormalization group in quantum field theory. In: ’t Hooft, G. (ed.) Under the Spell of the Gauge Principle. World Scientific, Singapore (1994)
Weinberg, S.: New approach to the renormalization group. Phys. Rev. D 8, 3497 (1973)
Veltman, M.J.G.: The infrared-ultraviolet connection. Acta Phys. Polon. B 12, 437 (1981)
’t Hooft, G.: Naturalness, chiral symmetry and spontaneous chiral symmetry breaking. In: ’t Hooft, G. (ed.) Under the Spell of the Gauge Principle. World Scientific, Singapore (1994)
Georgi, H.: Effective field theory. Ann. Rev. Nucl. Part. Sci. 43, 209 (1993)
Polchinski, J.: Effective field theory and the fermi surface. In: Harvey, J., Polchinski, J. (eds.) Recent Directions in Particle Theory: from superstrings and Black Holes to the Standard Model. World Scientific, Singapore (1993) [arXiv:hep-th/9210046]
Kaplan, D.: Five Lectures on Effective Field Theory, Lectures Delivered at the 17th National Nuclear Physics Summer School, Berkeley (2005) [arXiv:nucl-th/0510023]
Burgess, C.P.: Introduction to effective field theory. Ann. Rev. Nucl. Part. Sci. 57, 329 (2007) [arXiv:hep-th/0701053]
Kaplan, D.B.: Effective field theories, lectures at the 7th Summer School in Nuclear Physics, Seattle (1995) [arXiv:nucl-th/9506035]
Manohar, A.V.: Effective field theories. In: Latal, H., Schweiger, W. (eds.) Perturbative and Nonperturbative Aspects of Quantum Field Theory. Springer, Berlin (1997) [arXiv:hep-ph/9606222]
Pich, A.: Effective field theory. In: Gupta, R., Morel, A., de Rafael, E., David, F. (eds.) Probing The Standard Model Of Particle Interactions. Elsevier, Amsterdam (1999) [arXiv:hep-ph/9806303]
Dirac, P.A.M.: A new basis for cosmology. Proc. Roy. Soc. A 165, 199 (1938)
Nelson, P.: Naturalness in theoretical physics. Am. Sci. 73, 60 (1985)
Giudice, G.F.: Naturally speaking: the naturalness criterion and physics at the LHC. In: Kane, G., Pierce, A. (eds.) Perspectives on LHC Physics. World Scientific, Singapore (2008) [arXiv:0801.2562 [hep-ph]]
Wilson, K.G.: The renormalization group and strong interactions. Phys. Rev. D 3, 1818 (1971)
Susskind, L.: Dynamics of spontaneous symmetry breaking in the Weinberg–Salam theory. Phys. Rev. D 20, 2619 (1979)
Weinberg, S.: Anthropic bound on the cosmological constant. Phys. Rev. Lett. 59, 2607 (1987)
Susskind, L.: The anthropic landscape of string theory. In: Carr, B. (ed.) Universe or Multiverse? Cambridge University Press, Cambridge 2007 [arXiv:hep-th/0302219]
Polchinski, J.: The cosmological constant and the string landscape. In: Gross, D., Henneaux, M., Sevrin, A. (eds.) The Quantum Structure of Space and Time. World Scientific, Singapore (2007) [arXiv:hep-th/0603249]
Appelquist, T., Carazzone, J.: Infrared singularities and massive fields. Phys. Rev. D 11, 2856 (1975)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Álvarez-Gaumé, L., Vázquez-Mozo, M.Á. (2012). Effective Field Theories and Naturalness. In: An Invitation to Quantum Field Theory. Lecture Notes in Physics, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23728-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-23728-7_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23727-0
Online ISBN: 978-3-642-23728-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)