# Hypermomentum & Belinfante-Rosenfeld: Same Object?

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• mhob
In summary, the conversation discusses the variational theory of a perfect fluid with intrinsic hypermomentum, as well as the Belinfante-Rosenfeld tensor and the inertia principle. The theory is developed and equations of motion are derived for the fluid, along with expressions for its matter currents. The conversation also mentions the violation of the center of mass motion theorem for isolated systems with spin and the role of spin as a source of the gravitational field in general relativity.
mhob
Are they the same object?

Last edited:
I know what the second thing is, but what is the first? Please, provide the link to the literature.

The variational theory of perfect fluid with intrinsic hypermomentum in space-time with nonmetricity
O. V. Babourova, B. N. Frolov (Department of Mathematics, Moscow State Pedagogical University)
(Submitted on 6 Sep 1995)
The variational theory of the perfect fluid with an intrinsic hypermomentum is developed. The Lagrangian density of such fluid is stated and the equations of motion of the fluid and the evolution equation of the hypermomentum tensor are derived. The expressions of the matter currents of the fluid (the metric stress-energy 4-form, the canonical energy-momentum 3-form and the hypermomentum 3-form) are obtained.

Belinfante-Rosenfeld tensor and the inertia principle
Rodrigo Medina, J.Stephany
(Submitted on 13 Apr 2014)
In a recent letter we show that for an isolated system with a non symmetric energy momentum tensor the usual forms of the center of mass motion theorem are not valid. This was illustrated with a particular configuration of a magnet and a point charge for which it was shown that what is usually regarded as the center of mass of the system does not remain stationary even if the system is isolated. In a subsequent work we demonstrated that the violation of the center of mass motion theorem for isolated systems with spin is a direct consequence of the conservation of total angular momentum. We also show that there exists a generalized center of mass and spin which moves with constant velocity. In this letter we show that this center of mass and spin corresponds to the center of mass defined by the Belinfante-Rosenfeld tensor. We also show that, if the spin density instead of being of microscopic origin appears by a scaling process, the macroscopic Belinfante-Rosenfeld tensor emerges from the average of the microscopic energy-momentum tensor as the true macroscopic energy momentum tensor. This implies that in general spin has to be considered as a source of the gravitational field in general relativity

## 1. What is hypermomentum?

Hypermomentum is defined as a quantity that describes the motion of an object, taking into account both its linear and angular momentum. It takes into consideration the rotational movement of an object in addition to its linear movement, and is often used in the study of complex systems with multiple components.

## 2. What is Belinfante-Rosenfeld tensor?

The Belinfante-Rosenfeld tensor is a mathematical construct used in the theory of relativity to describe the energy, momentum, and angular momentum of a physical system. It is a symmetric rank-2 tensor that is conserved under Lorentz transformations and is often used in the study of quantum field theory.

## 3. How are hypermomentum and Belinfante-Rosenfeld tensor related?

Hypermomentum and the Belinfante-Rosenfeld tensor are two different concepts that describe the same physical object. While hypermomentum takes into account both linear and angular momentum, the Belinfante-Rosenfeld tensor describes the energy and momentum of a system in a relativistic framework. They are mathematically related through a specific transformation, known as the Belinfante-Rosenfeld transformation, which allows for the calculation of the hypermomentum using the Belinfante-Rosenfeld tensor.

## 4. What are the applications of hypermomentum and Belinfante-Rosenfeld tensor?

Both hypermomentum and the Belinfante-Rosenfeld tensor have important applications in the fields of physics and engineering. They are used in the study of complex systems, such as in fluid dynamics and quantum mechanics, and have practical applications in the design of advanced technology, such as spacecraft and advanced materials.

## 5. What are the implications of the fact that hypermomentum and Belinfante-Rosenfeld tensor describe the same object?

The fact that hypermomentum and the Belinfante-Rosenfeld tensor describe the same physical object has significant implications for our understanding of the fundamental laws of physics. It highlights the deep connections between different branches of physics, such as classical mechanics and relativity, and allows for a more comprehensive understanding of complex systems. It also has practical implications for the development of advanced technologies that rely on a deep understanding of the underlying physical principles.

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