Effective Field Theory, Past and Future (0908.1964v3)

Abstract: This is a written version of the opening talk at the 6th International Workshop on Chiral Dynamics, at the University of Bern, Switzerland, July 6, 2009, to be published in the proceedings of the Workshop. In it, I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

• The paper demonstrates that effective field theories provide a general framework for deriving the S-matrix consistent with fundamental symmetry principles.
• It outlines the evolution from current algebra to effective Lagrangians, enabling systematic treatments of strong and gravitational interactions.
• Weinberg speculates that these theories may underpin both the Standard Model and General Relativity, offering predictive insights into quantum gravity.

Overview of "Effective Field Theory, Past and Future" by Steven Weinberg

In "Effective Field Theory, Past and Future," Steven Weinberg presents a detailed examination of effective field theories, tracing their historical development and discussing their application to both strong interactions and gravity. This paper is adapted from a talk given at the 6th International Workshop on Chiral Dynamics. Weinberg contextualizes the role of effective field theories within the broader scope of theoretical physics, offering insights into their functionality and anticipates their future contributions.

Historical Development

Weinberg begins by recounting the emergence of effective field theories, notably from the perspective of strong interactions. He revisits the principle of spontaneously broken symmetries underlying the behavior of axial vector currents and the pion's Goldstone boson status, concepts initially advanced by Nambu. This foundation gave rise to current algebra, a set of techniques that succeeded without recourse to specific Lagrangians, exemplifying its effectiveness with the derivation of the Adler-Weisberger sum rule.

He elaborates on the transition from current algebra to the development of effective Lagrangians, notably his own contributions to non-linear realizations of chiral symmetry. Weinberg highlights the move from detailed current algebra results to the more systemic formulations allowed by effective field theories, primarily focusing on the pion-nucleon and pion-pion interactions.

Theoretical Implications

Weinberg introduces the radical concept of non-renormalizable theories as renormalizable when approached through effective field theory frameworks. This perspective, inspired by techniques in critical phenomena and Wilson's renormalization group approach, allowed for a perturbative treatment that accommodates all symmetry-allowed terms in an effective Lagrangian, rendering each theory viable beyond tree-level approximations.

An essential aspect of this discussion is Weinberg's "folk theorem," positing that effective field theories can describe the most general S-matrix consistent with overarching symmetry principles, cluster decomposition, and other standard assumptions of quantum field theory and S-matrix theory.

Applications and Extensions

The paper covers significant applications of effective field theories, extending them to various domains. Weinberg points out that effective field theory methodologies are not only applicable to low-energy strong interactions but have been wielded in areas such as nuclear forces and condensed matter physics, specifically in theories like BCS superconductivity.

Importantly, Weinberg speculates on the view that Standard Model and General Relativity may be parts of an overarching effective field theory, suggesting a connection to quantum gravitational phenomena and the potential integration with a high-energy regime, possibly string theory. He champions exploring non-renormalizable terms like those predicting observable neutrino oscillations which imply new physics at energy scales of $10^{16} \text{GeV}$.

Implications for Gravity

Highlighting recent developments, Weinberg explores the possibility of a quantum field theory for gravity that maintains coherence at all energy scales. He discusses various approaches to asymptotic safety in quantum gravity, including dimensional continuation, large N expansions, lattice methods, and truncated renormalization group equations. The results from such analyses suggest the potential for a finite-dimensional UV critical surface, lending predictability to high-energy gravitational physics.

Conclusion

Steven Weinberg's essay synthesizes decades of theoretical advancement into a coherent narrative on effective field theories. This work not only consolidates previous achievements but also casts an evaluative eye on future possibilities, particularly concerning gravity and high-energy physics. Weinberg's insights promise fertile ground for theoretical exploration, emphasizing the role of effective field theories in continually shaping our understanding of the universe.