Pair Creation and Backreaction in Strong Fields: An Amplitudes Perspective

Core Concepts

This paper revisits particle creation and backreaction in strong electromagnetic fields using an amplitudes-based approach, highlighting the importance of resummation and disconnected loop diagrams in going beyond the background field approximation.

Abstract

Bibliographic Information:

Copinger, P., Edwards, J. P., Ilderton, A., & Rajeev, K. (2024). Pair creation, backreaction, and resummation in strong fields. arXiv preprint arXiv:2411.06203.

Research Objective:

This paper aims to provide a systematic approach to understanding backreaction in strong field QED by analyzing particle creation and its effects on the electromagnetic field using an amplitudes perspective.

Methodology:

The authors utilize the framework of quantum field theory, specifically scalar QED, to model the interaction of a scalar field with a strong electromagnetic field represented by a coherent state of photons. They employ the Furry expansion to calculate scattering amplitudes and observables, focusing on the next-to-leading order contributions to capture backreaction effects.

Key Findings:

• The authors demonstrate that observables, such as the waveform and the number of produced photons, receive contributions from disconnected loop diagrams, highlighting the significance of these diagrams in strong field regimes.
• They show that converting between in-out (amplitude) and in-in (expectation value) expressions necessitates the resummation of an infinite number of disconnected loop diagrams.
• The study reveals that the asymptotic back-reacted field in a specific model of a time-dependent electric field exhibits damped oscillations.

Main Conclusions:

The amplitudes-based approach provides a comprehensive framework for studying backreaction in strong field QED, emphasizing the importance of resummation and disconnected loop diagrams. The findings have implications for understanding the behavior of strong electromagnetic fields in extreme environments, such as high-intensity laser experiments and astrophysical phenomena.

Significance:

This research contributes to the theoretical understanding of strong field QED by providing a systematic method for calculating backreaction effects. It has implications for the interpretation of experimental data from high-intensity laser facilities and for modeling astrophysical objects with strong electromagnetic fields.

Limitations and Future Research:

The study focuses on scalar QED, and extending the analysis to full QED with spinor electrons and positrons would provide a more complete picture. Further research could explore higher-order corrections in the Furry expansion and investigate the impact of backreaction on other observables, such as particle spectra and polarization.

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Pair creation, backreaction, and resummation in strong fields

by Patrick Copi... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.06203.pdf

Deeper Inquiries

How can the amplitudes-based approach be extended to incorporate the effects of spin and other fundamental particle interactions in strong field QED?

Extending the amplitudes-based approach to incorporate spin and other interactions in strong field QED involves several key modifications while preserving the fundamental principles outlined in the context. Here's a breakdown:

Spin Effects:

Dirac Fermions: Instead of scalar QED, the theory must be upgraded to spinor QED, employing the Dirac equation to describe fermions. This introduces spin degrees of freedom, leading to modified Feynman rules for vertices and propagators. For instance, the electron-photon vertex now includes a gamma matrix, coupling the photon to the electron's spin.
Polarization States: Photons, as spin-1 particles, possess two polarization states. These need to be explicitly accounted for in the coherent state description of the strong field and in the calculation of amplitudes. Summing over final state photon polarizations and averaging over initial state polarizations becomes necessary.
Spin-Dependent Interactions: The presence of spin introduces new interaction terms in the Lagrangian. For example, in addition to the minimal coupling between the photon and the fermion current, we might have terms like the Pauli term, representing the interaction of the fermion's magnetic moment with the electromagnetic field.

Other Interactions:

Weak Interactions: Incorporating weak interactions requires extending the gauge group of the theory to include the weak force bosons (W and Z bosons). This introduces new Feynman rules for weak interaction vertices and propagators. The interplay between strong electromagnetic fields and weak interactions can lead to novel phenomena like flavor oscillations in the presence of strong fields.
Beyond Standard Model Physics: The framework can be further extended to include hypothetical particles and interactions beyond the Standard Model. For instance, if we consider axion-like particles, their coupling to the electromagnetic field can be studied in the strong field regime using modified Feynman rules.

Computational Challenges:

Increased Complexity: Including spin and additional interactions significantly increases the complexity of the calculations. The number of diagrams and the algebraic manipulations involved grow substantially.
Gauge Invariance: Maintaining gauge invariance becomes more intricate with spin and additional interactions. Careful consideration of gauge-fixing procedures and Ward identities is crucial to ensure the consistency of the calculations.

In summary, extending the amplitudes-based approach to incorporate spin and other interactions in strong field QED requires a careful upgrade of the theoretical framework, including modified Feynman rules, explicit treatment of polarization states, and consideration of new interaction terms. While computationally more challenging, this approach provides a powerful tool for investigating the rich interplay of fundamental forces in extreme electromagnetic environments.

Could the observed damped oscillations in the back-reacted field have implications for the long-term stability of strong electromagnetic fields in astrophysical settings?

The observed damped oscillations in the back-reacted field, as described in the context, could indeed have intriguing implications for the long-term stability of strong electromagnetic fields in astrophysical settings. Here's an exploration of the potential connections:

Energy Dissipation: The damping of the oscillations suggests energy dissipation from the electromagnetic field. In the context of the calculation, this energy is transferred to the created electron-positron pairs. In astrophysical environments, this energy could potentially heat the surrounding plasma or be radiated away as lower-energy photons.

Field Decay: The damped oscillations hint at a mechanism for the decay of strong electromagnetic fields over time. While classical electromagnetism predicts stable electromagnetic fields, quantum effects like pair production provide a pathway for energy loss and eventual field decay.

Astrophysical Implications:

Pulsars: Pulsars, highly magnetized rotating neutron stars, possess some of the strongest electromagnetic fields in the universe. The damped oscillations suggest that even these extreme fields might not be eternally stable and could decay over very long timescales due to quantum effects.
Magnetars: Magnetars, a type of neutron star with even stronger magnetic fields than pulsars, could be significantly affected. The decay of their magnetic fields through pair production could contribute to their observed X-ray and gamma-ray emissions.
Early Universe: In the extremely hot and dense conditions of the early universe, strong electromagnetic fields are believed to have played a role in various cosmological processes. Understanding their stability and decay mechanisms is crucial for accurate modeling of the early universe.

Further Considerations:

Plasma Effects: In realistic astrophysical settings, the presence of plasma (charged particles) surrounding strong electromagnetic fields would introduce additional complexities. Plasma screening, collisions, and collective effects could influence the field decay rate and potentially lead to different oscillation patterns.
General Relativity: For extremely strong fields, general relativistic effects might become significant. The curvature of spacetime near massive objects could alter the dynamics of pair production and field decay.

In conclusion, while the observed damped oscillations provide a theoretical basis for the decay of strong electromagnetic fields, further research incorporating astrophysical realities like plasma effects and general relativity is necessary to fully assess their implications for the long-term stability of these fields in astrophysical environments.

What are the potential connections between the resummation techniques employed in this study and other areas of theoretical physics, such as condensed matter physics or cosmology?

The resummation techniques employed in the study of strong field QED, particularly in the context of pair creation and backreaction, find intriguing parallels and potential applications in diverse areas of theoretical physics, including condensed matter physics and cosmology. Here's an exploration of these connections:
Condensed Matter Physics:

Schwinger Effect Analogues: The Schwinger effect, pair production from a strong electric field, has analogues in condensed matter systems. For instance, in graphene, a two-dimensional material with relativistic-like electrons, applying a strong electric field can lead to electron-hole pair creation, mimicking the Schwinger effect. The resummation techniques used to study pair production in QED could be adapted to analyze these condensed matter analogues, providing insights into the non-perturbative behavior of these systems.

Non-Equilibrium Phenomena: Strong field QED often deals with systems far from equilibrium, where particle creation and annihilation processes are significant. Similar situations arise in condensed matter physics, for example, in driven systems or during phase transitions. The resummation methods developed for strong field QED could offer valuable tools for studying non-equilibrium dynamics and critical phenomena in condensed matter.

Cosmology:

Early Universe Physics: As mentioned earlier, strong electromagnetic fields are believed to have been present in the early universe. The resummation techniques used to handle backreaction in strong field QED could be relevant for understanding the evolution of these fields and their potential impact on cosmological processes like baryogenesis (the generation of matter-antimatter asymmetry) and inflation (a period of rapid expansion in the early universe).

False Vacuum Decay: The concept of vacuum instability and decay, central to the study of the Schwinger effect, also appears in cosmology in the context of false vacuum decay. This process, where the universe transitions from a metastable vacuum state to a lower-energy vacuum, is thought to be relevant for understanding the early universe and the formation of cosmic structures. The resummation methods used to analyze vacuum decay in strong field QED could provide insights into the dynamics of false vacuum decay in cosmology.

General Themes:
Beyond specific examples, several general themes connect the resummation techniques across these fields:

Non-Perturbative Physics: Resummation techniques are often essential for studying non-perturbative phenomena, where traditional perturbative expansions break down. This is a common thread linking strong field QED, certain condensed matter systems, and aspects of cosmology.
Effective Field Theories: Resummation methods are closely related to the development of effective field theories, which capture the essential physics at a particular energy scale. This approach is widely used in condensed matter physics and cosmology to simplify calculations and extract universal behavior.
Computational Techniques: The computational techniques developed for resummation in strong field QED, such as path integral methods and functional determinants, have broader applicability in other areas of theoretical physics.
In summary, the resummation techniques employed in strong field QED, initially developed to address the challenges of pair creation and backreaction, have the potential to transcend their original domain and provide valuable insights into non-perturbative phenomena, non-equilibrium dynamics, and vacuum instability in diverse areas of theoretical physics, including condensed matter physics and cosmology.