Core Concepts

This article provides a retrospective on the early development of string theory, reviews the viable 3-3-1 model as a potential replacement for the Standard Model, and speculates on the principles that may have led Nature to select the Standard Model or the 3-3-1 model. It also discusses the author's recent work on deriving classical theories from a functional integral formulation without the imaginary unit i.

Abstract

The article begins by recounting the early work on the Veneziano model and the factorization that led to the discovery of string theory, with Paul Frampton and Yoichiro Nambu playing key roles. It then reviews the 3-3-1 model, which Frampton developed as a possible extension of the Standard Model that could resolve the issue of triangle anomalies. The author speculates on various principles, such as the number of families, the simplicity of representations, the structure of the gauge group, and the connections between the Lie algebras, that may have guided Nature's selection of the Standard Model over the 3-3-1 model.

The article then discusses the idea of primordial black holes as a potential dark matter candidate, noting the author's disagreement with Frampton's preference for this model. The final section focuses on the author's own recent work, which attempts to derive classical theories from a functional integral formulation without the imaginary unit i, and how this could lead to predictions about the cosmological constant and the prevalence of black holes.

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arxiv.org

Stats

"The 3-3-1 model has the feature, via the disappearance of anomalies, needing (a multiple of) three families."
"The Standard Model has a quantization rule for the U(1) charge usually called y/2, which relates it to both the representation of the color SU(3)c and the weak SU(2) requiring 'triality' for SU(3)c + sW + y/2 = 0 (mod 1)."
"Primordial black holes lighter than 1015g = 1012 kg would have radiated away or would be just about doing it today."

Quotes

"If really we ask for such a maximal action, then the solution would be somewhat bad, because the kinetic energy is not bounded from above."
"Now, the galaxies, etc., have run so far away that they have run most of their original speed off in the sense that the Hubble–Lemaitre expansion has dropped very much compared to the original one, say at the end of inﬂation."
"Thus, indeed, the prediction is that Λ = 0."

Key Insights Distilled From

by Holger B. Ni... at **arxiv.org** 10-01-2024

Deeper Inquiries

The principles outlined in the article, particularly regarding the number of families and the structure of the gauge group, play a crucial role in guiding the search for a more fundamental theory beyond the Standard Model (SM) and the 3-3-1 model. The requirement for a multiple of three families in the 3-3-1 model, as a means to cancel anomalies, suggests that any viable theory must adhere to specific symmetry and representation constraints. This principle could lead researchers to explore theories that inherently predict the number of families, potentially pointing towards a deeper underlying symmetry or mechanism that governs particle interactions.
Moreover, the structure of the gauge group, particularly the use of SU(3) in both color and weak interactions, raises questions about the nature of gauge symmetries in a more fundamental theory. The article suggests that a deeper theory might favor simpler gauge groups or a unification of gauge groups at higher energy scales. This could inspire investigations into grand unified theories (GUTs) or string theory frameworks that incorporate these principles, potentially leading to a more comprehensive understanding of particle physics and the fundamental forces.

The apparent contradictions between the DAMA-LIBRA experiment and other dark matter search results, such as those from the Anais experiment, can be addressed through several alternative explanations or models. One possibility is the existence of multiple dark matter components, where DAMA-LIBRA detects a specific type of dark matter particle that interacts differently than those searched for in other experiments. This could imply that dark matter is not a single entity but rather a collection of particles with varying properties.
Another explanation could involve the influence of environmental factors on dark matter detection. The article mentions that DAMA-LIBRA is located 1400 meters underground, which may affect the interaction rates of dark matter particles compared to experiments situated closer to the surface. This suggests that the detection rates could vary based on the depth and geological conditions, leading to discrepancies in results.
Additionally, models that incorporate new physics, such as interactions with other fields or particles, could provide a framework for reconciling these differences. For instance, if dark matter particles exhibit non-standard interactions or if there are additional forces at play, this could alter the expected detection rates in different experimental setups.

The author's exploration of deriving classical theories from a functional integral formulation without the imaginary unit i presents intriguing possibilities for extending this approach to other areas of theoretical physics. One potential application is in quantum field theory (QFT), where the conventional use of the imaginary unit in the path integral formulation is fundamental. By removing i, researchers could investigate alternative formulations of QFT that might yield new insights into particle interactions and the nature of quantum fields.
Furthermore, this approach could be applied to the study of quantum gravity, where the complexities of combining general relativity with quantum mechanics often lead to divergences and ambiguities. A functional integral formulation without i might provide a novel perspective on the dynamics of spacetime and the behavior of gravitational fields at quantum scales, potentially leading to a more coherent theory of quantum gravity.
Additionally, the principles derived from this work could inform the development of effective field theories in condensed matter physics, where the interplay between classical and quantum behaviors is crucial. By applying the insights gained from the functional integral approach, researchers could explore new models that better capture the emergent phenomena observed in complex systems.
In summary, the author's work opens avenues for rethinking foundational concepts in various fields of theoretical physics, encouraging a reevaluation of established frameworks and potentially leading to groundbreaking discoveries.

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