Scalar Thermal Field Theory for a Rotating Plasma (2503.09677v2)

Abstract: In this paper it is initiated the systematic study of thermal field theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. The focus here is on scalar fields, although some results also apply to fields with arbitrary spins. A general technique to compute ensemble averages is provided. Moreover, path-integral methods are developed to study thermal Green's functions (with an arbitrary number of points) in generic theories, which cover both the real-time and imaginary-time formalism. It is shown that, while the average angular momentum, like the chemical potentials, does not contribute positively to the Euclidean action, its negative contributions can be compensated by some other contributions that are instead positive, at least in some cases. As an application of the developed general formalism, it is shown that the production of particles weakly coupled to a rotating plasma can be significantly enhanced compared to the non-rotating case. The Higgs boson production through a portal coupling to a dark sector in the early universe is studied in some detail. The findings of this paper can also be useful, for example, to investigate the physics of rotating stars, ordinary and primordial black holes and more exotic compact objects.

Scalar Thermal Field Theory for a Rotating Plasma: An Analytical Study

The paper Scalar Thermal Field Theory for a Rotating Plasma by Alberto Salvio presents a comprehensive paper on the formulation of thermal field theory (TFT) in the context of a rotating plasma. By introducing a general framework applicable to arbitrary equilibrium density matrices, this work significantly expands on traditional TFT applications, integrating effects of temperature, chemical potentials, and angular momentum.

Framework and Methodology

The paper begins by establishing a general form for the equilibrium density matrix that includes contributions from both chemical potentials and average angular momentum. Salvio shows how to simplify this matrix in a frame where the plasma is at rest, essentially reducing it to a function of commuting operators. This simplification is crucial for subsequent calculations of ensemble averages of quantum observables such as energy, angular momentum, and charge distributions.

For non-interacting particles, the paper successfully calculates ensemble averages, demonstrating how chemical potentials and rotational effects can be incorporated into the statistical mechanics of the system. Particularly notable is the analysis of the convergence of these averages, leading to an important condition for the rotational velocity parameter, $v$, to be less than the speed of light to ensure finite averages.

Numerical and Analytical Results

Salvio extends the analysis to the computation of "non-time-ordered" two-point functions for free fields, serving as a building block for more complex calculations involving interactions. This work includes a closed form for free field propagators under the influence of rotation and chemical potentials. This technical advancement is instrumental for perturbative calculations in TFT when interactions are considered.

For interacting theories, the author derives path-integral expressions for the partition function and thermal Green's functions that factor in rotational effects. He follows this with a transformation to a Lagrangian formulation that provides a way to perform these calculations in practice, especially when ordinary scalar fields are involved. This transformation also highlights the challenge posed by rotation: while rotation contributes negatively to the Euclidean action, these contributions can be positively offset by other factors in certain cases.

Applications and Implications

An application explored through this formalism is the computation of particle production rates from a rotating plasma. Using a real-time formalism and focusing on a weakly-coupled particle scenario, Salvio derives a general expression for the production rate of spin-0 particles, exemplified by Higgs production in a rotating dark plasma via a scalar portal interaction. This example showcases the utility of the developed theoretical framework in modeling real physical processes, including those occurring around astrophysical objects like rotating stars or black holes.

Salvio's analysis also reveals how rotational effects can significantly enhance production rates. Specifically, the paper demonstrates that as the rotational velocity parameter approaches the speed of light, production rates increase indefinitely. This insight has profound implications for understanding particle dynamics in high-energy environments.

Future Outlook

The paper lays a foundation for further exploration of scalar TFT in more complex scenarios, potentially involving higher spin fields or non-linear interactions. Additionally, the methods developed could inspire investigations into non-perturbative phenomena using lattice approaches, despite the known challenges with sign problems in Euclidean settings.

Ultimately, this work pushes the boundaries of TFT by systematically incorporating rotational effects, opening new avenues for theoretical and computational advancements in understanding thermal plasmas in both laboratory and cosmic settings. The compelling combination of analytical techniques and numerical insights marks a significant contribution to the field of thermal quantum field theory, offering a framework capable of tackling various high-energy physics and astrophysical challenges.