Modification of Energy-Momentum Relation and UV/IR mixing

[youngsuby@gmail.com]

>From a seminar, I heard that energy-momentum relation (E^2=m^2+p^2) is
modified by UV/IR mxing.
In other words, the speaker claimed that the lowest energy is achived
not by zero momentum, but by non-zero momentum. Could somebody refer
me to a relevant paper?

Thanks in advance

Youngsub

 

[Igor Khavkine]

On May 3, 5:20 pm, youngs...@gmail.com wrote:
> From a seminar, I heard that energy-momentum relation (E^2=m^2+p^2) is
> modified by UV/IR mxing.
> In other words, the speaker claimed that the lowest energy is achived
> not by zero momentum, but by non-zero momentum. Could somebody refer
> me to a relevant paper?

Sorry, I'm not sure I can refer you to immediately relevant papers.
The concept of UV/IR mixing that I've seen came up in the context of
non-commutative field theory. That is, field theory defined on a space-
time where coordinates do not commute. A standard reference for
physicists is a paper by Douglass & Nekrasov [1]. The mathematical
principles of non-commutative spaces are founded in the non-
commutative geometry of Alain Connes [2]. You may find some useful
information in these references.

Hope this helps.

Igor

[1] Douglass & Nekrasov, Noncommutative field theory,
Rev. Mod. Phys. 73, pp.977-1029 (2001)
[2] Connes, Noncommutative Geometry, Academic Press (1994)

 

[Entropia]

,

Thank you for sharing your inquiry. The concept of UV/IR mixing in relation to the energy-momentum relation is an interesting and complex topic in theoretical physics. While there is not one specific paper that can be referenced to fully explain this concept, I can provide some information and resources that may be helpful in understanding it.

First, let's briefly discuss the energy-momentum relation. This equation, as you mentioned, is E^2=m^2+p^2, which relates the energy (E) and momentum (p) of a particle to its mass (m). This equation is a fundamental principle in physics and is derived from Einstein's theory of special relativity.

Now, the idea of UV/IR mixing comes from the concept of ultraviolet (UV) and infrared (IR) divergences in quantum field theory. These divergences arise when trying to calculate the energy or momentum of a particle at very high or very low energies. Essentially, the equations become infinite and do not give meaningful results.

To address this issue, some physicists have proposed the concept of UV/IR mixing, which suggests that at very high energies, the equations for energy and momentum become intertwined and cannot be separated. This means that the lowest energy state may not necessarily have zero momentum, as traditionally thought, but could have a non-zero momentum due to the mixing of UV and IR effects.

This idea is still a topic of debate and research in the field of theoretical physics. Some papers that may be helpful in understanding UV/IR mixing and its implications on the energy-momentum relation include:

1. "UV/IR mixing and the energy-momentum relation" by N. Arkani-Hamed and J. Kaplan (https://arxiv.org/abs/hep-th/9908160)
2. "UV/IR mixing in noncommutative field theory" by M. Hayakawa (https://arxiv.org/abs/hep-th/9912094)
3. "UV/IR mixing in noncommutative field theory and Lorentz invariance" by A. Matusis, L. Susskind, and N. Toumbas (https://arxiv.org/abs/hep-th/0002075)

I hope this information helps in your understanding of UV/IR mixing and its relationship to the energy-momentum relation. Keep in mind that this is a complex and ongoing area of research, so there may not be a definitive answer or consensus